Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=6.1 and x=1.4  and passes through the point (0,3.3).

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

A:

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

A: Here given an equation of the parabola

Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

A:

Q: Sketch the parabola f (x) = 2x2 - 4x.

A: Given: f(x) = 2x2-4x To sketch: The given parabola.

Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of (0, 231), which…

A:

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: Find the vertex of the parabola. f(x) = 2x + 16x + 39 (х, у) %3

A: We have to find vertex

Q: ,2 The vertex of the parabola of f(x)=x²+x is

A: Equation of the parabola :y=a(x-h)2+kwhere (h,k) = vertex of the parabola

Q: Find the function f whose graph is obtained by shifting the parabola y = x 2 by 3 units to the right…

A: Given the graph of the parabola y=x2 is shifted by 3 units to the right and 4 units down shown in…

Q: Find the quadratic function y=ax+bx+ c whose graph passes through the given points (3,29), (2,-26),…

A: We have been given three ordered points and we need to find a quadratic function passing through…

Q: A conservation commission estimates the reproduction function for rainbow trout in a large lake to…

A: Given:

Q: What is the axis of symmetry for the following quadratic function? y = -4 Oy = -1 x = -4 Dx = -1

A: Given graph of a quadratic function

Q: Write the equation of the parabola that has the same shape as f(x) = 3x² but with vertex (7,6) in…

A:

Q: Consider f(x)=ax3+bx2+cx+d Under what conditions on a,b,c,and d does the graph of a cubic function…

A:

Q: # 3) Create the equation of the cubic, in standard form, that has x-intercepts of 3, -1, and 2…

A:

Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Determine the vertex for the following parabola. f (x) = 7x2 + 3x – 4 -

A:

Q: Please confirm if the selected answer is correct ?

A:

Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

A:

Q: find the points on the parabola y=x^2 closest to the point (0,1)

A:

Q: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

A:

Q: The following table shows the cost C of traffic accidents, in cents per vehicle-mile, as a function…

A: Given:   Speed (s) Cost ( c) 20 1.3 25 0.4 30 0.1 35 0.3 40 0.9 45 2.2 50 5.8

Q: Sketch the graphs of the following cubic functions, showing x-axis intercepts  a y = −(2 − x)(x +…

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

Q: Show that, for any cubic function of the form y = ax + bx² + cx + d, %3D there is a single point of…

A:

Q: Identify the equation of a parabola with a minimum value of 1. O f(x) = -(z - 2)² + 3 O f(z) = -2(x…

A: The general equation of a parabola with vertex at a point (x,y) is given by the equation;…

Q: Write the equation of the parabola that has the same shape as f(x) = - 4x but with vertex (7,3) in…

A:

Q: If the vertex of the parabola f (x)= x² +bx+c is at (7, -4), find b and c. (Note: a = 1).

A:

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

A:

Q: Let f (x) = 1x² +6x+8. Find the x-coordinate for the parabola's vertex. Round your answer to the…

A:

Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: Prove that if a parabola crosses the x-axis twice, the x-coordinate of the vertex of the parabola is…

A: Since, we have to prove that if parabola crosses the x-axis twice, the x-coordinate of the vertex of…

Q: The table shows projections for the female population of a country (in millions). Year 2020 2045…

A: Here is the solution,

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

A:

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

A: We have to find the coordinates of the vertex for the parabola defined by the quadratic function…

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

A: The equation for a parabola is written in vertex form as, In vertex form the vertex is given as…

Q: The table shows projections for the female population of a country (in millions). Year 2015 2035…

A:

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

A:

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: 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: 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: The parabola y = Px² + Qx + R_passes through the coordinate (1,1) and has b. Determine the values of…

A:

Q: Find the coordinates of the vertex for the parabola defined by the quadratic function f (x) = 3(x…

A: Given function is  fx=3x+52−4

Q: What is the correct quadratic function for this parabola?

A: Note: General equation of parabola is y-k = 4a(x-h)^2 and x-h = 4a(y-k)^2  Vertex for both the form…

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

A:

Q: Express the equation of the parabola below in standard form. x2+6x−2y+1=0

A: Recall: Equation of parabola:         y-k2=4ax-h where (h,k) is the vertex and parabola is open in…

Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

A:

Q: Write the equation of the parabola that has the same shape as f(x) = - 4x but with vertex (7,3) in…

A: The solution is as shown below

Q: Find the vertex for the parabola y = 0.01x2 + 0.6x + 100. Then determine a reasonable viewing…

A: Given: y=0.01x2+0.6x+100  To determine: The vertex for the given parabola & graph of the given…