3.4 A) Sketch a possible graph of a quadratic function which has two complex roots, a graph that opens upwards, and a y intercept of (0,2).   B) Sketch a possible graph of a quadratic function which has two real roots (one positive, one negative), a graph that opens downwards, and y-intercept at (0,4). C) Sketch a possible graph of a quadratic function, whose discriminant is 0 and its graph open upwards.

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: t if the complex number z is a root of the polynomial f(

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Q: The parabola y = - 16 (X – 2)- -+1 has its fócus at (2, -3). Determine and state the equation of the…

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Q: Express x2 – 12x + 16y – 60 = 0 to standard form and construct the parabola

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Q: The equation of the parabola that has a vertical axis of symmetry, touches the x-axis and has its…

A: Given, The parabola has vertical axis of symmetry touches the x axis and has its focus at 1, 7 We…

Q: The vertex of the parabola f(z) = + 6z + 7 is O (-3,-2) O (-6,-18) O (-6, -2) O (-3,5) O (-9,-2)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Determine the value of p (where |p| corresponds to the distance from the vertex to the focus) of the…

A: Given: Parabola whose vertex is 6, 7 and the x-intercepts are 3, 0 and 9, 0. To determine: Value of…

Q: 15 2. Find the equation of a parabola through(-, 2) and (0,–1) whose axis is parallel 4 to the…

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Q: Consider the graphs of equations of the quadratic form = ax² + bx + c that have two x-intercepts.…

A: First, we will plot the graph of quadratic equation ax2+bx+c=0.    Axis of parabola i.e. axis of…

Q: 11. Find all three roots of the following cubies by first reducing them to cubics without an r²…

A: Given the cubic equation

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: find an equation for the the parabola has its vertex at the origin and satisfies the given condition…

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: The vertex of the parabola f(x) =(x+3) - 4 is а) (-3, -4) b) (3, -4) с) (3, 4) d) (-3, 4)

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Q: 9. Find the equation in factored form for a parabola that has zeros -4, and 8, and passes through…

A: let the general equation of parabola is y=ax2+bx+c -4 is one of the zero of the parabola ,…

Q: 17. Two parabolas have functions given by f(x) = -.5z? + 2x + 4and g(r) = 3z2 + 4x + 2 Find the…

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Q: 5) Find the equation for the parabola that has its vertex at (5,-3), axis parallel to the y-axis,…

A: given,         vertex of parabola =5,-3  and passing through the point 9,5

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: We have Vertex=(0,0)Directrix x=-15

Q: The vertex of the parabola f(x) = – 2(x+2) - 3, is O a. (2, 3) Ob.(-2, -3) OC (2, -3) O d. (-2, 3)

A: As per the company guidelines we can solve one question. I hope that the given solution will help…

Q: Example 10. Use Desmos to graph the following quadratic relation y = -2x² + 8x. Describe the…

A: The graph is shown below:

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: find the equation of a parabola vertex=(0,0) and directrix x=-4

Q: 2. (a) Bring the quadratic function f(x) 1 x² + 3x 5 into the standard form and identify the axis of…

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Q: 5. Find the equation of the parabola that has a horizontal axis of symmetry, passing through the…

A: the general equation of a parabola is x=ay2+by+c                            (1) horizontal axis…

Q: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: 5. Find the equation of the following parabola in standard form: f(x) =

A: Given: From the given graph of the parabola, it intersects the x-axis at x=1 & x=3, so it has…

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given query is to find the equation of the paraola.

Q: List the roots of the parabola: y = x² + 2x + 5 In other words, list the solutions of the equation:…

A: The roots of a quadratics equation ax2+bx+c=0 is given by, x=-b±b2-4ac2a

Q: 8. Find the function that will generate the points on a parabola that opens down, has a base of 4…

A: A parabola has base 4 and height 6

Q: 4. Find the equation of a parabola with axis parallel to the y-axis and passing through ( ). G. 3…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 5. A parabola has its turning point at x = -4 and one of the x-intercepts is x= -3. Ба What is the x…

A: From the given data: Parabola has a turning point at x=-4 That is x-coordinate of the vertex is…

Q: Determine the vertex of each parabola. 1. f(x) = x² + 2x – 15 - axis of symmetry: x = -1

A: We have to find vertex

Q: 8.44.) In Ax² + Cy² + Dx + Ey +F = 0, show that if A and C have the same signs, then the graph of…

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

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Q: On a separate piece of paper, sketch the graph of the parabola f(x) = x² + 9. On the same set of…

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Q: 5. Given the following parabola, f, -5 -4 -3 -2 -1 -6-5 -4 3-2 -1, 0 1 234 5/ 67 -2 -3 -6

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)…

A: The quadratic function is given by fx = 2x-32+1 To evaluate : The vertex of the parabola defined by…

Q: 7. Write an equation for each parabola a) 0, 11) 8- 4- (4, –5) b) | YA |(-6, 4) 4- (-5.3) 2 -6 -2 0…

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Q: a) Suppose that 5, 2, and 3 are the solutions of a cubic equation. Sketch a graph of the…

A: Topic:- polynomial function

Q: Find an equation for the parabola shown in the figure.

A: Given: The focus F-2,1 and directrix x=3 of the parabola, To find: The equation of the parabola.

Q: 1. Describe an algebraic method for determining the x-intercepts, if any, of a parabola which…

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Q: If a is greater than or equal to zero the equation of the parabola is of the form?

A: Parabola is a three dimensional curve, where any point is at fix distance from the point called…

Q: 5. Find the equation of the parabola in standard form with a directrix located 5 units below the…

A: The standard equation of the parabola is (x-h)2=4a(y=k) Where (h,k) is the vertex Here h=3, k=-2…

Q: Write equation 16x2 - 24xy + 9y2 - 60x - 80y + 100 = 0 as a quadratic equation in y and then use the…

A: We need to use a graphing utility to graph the following exercise Given quadratic equation…

Q: Find the equation for the parabola that has its vertex at the origin and has directrix at…

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Q: The vertex of the parabola f(x) = a+ 14z + 10 is %3D о (-14, -63) о (-21, -39) о (-14, -39) о (-7,…

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Q: The a value in the function f(x) = 2x2 makes the parabola %3D O more wider moves it left

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Q: Find an equation for the parabola that has its vertex at the origin and has a directric at x=1/29

A: We want to find out the equation of the parabola.

Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

A:

Q: The parabola x² - 2x + 2y + 7 = 0, has a vertex at (1,3). O(-1,3). O (-1,-3). O (1,-3).

A: Suppose the equation of a parabola is of the form  y=ax2+bx+c where a, b and c are constants. The…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.