For the graph of the following equation: f(x) = - 3x² + 12x + 5 a) Is there a maximum or a minimum? (Choose one) b) What is the vertex? (provide coordinates) c) State the domain and range in interval notation. Domain: Range:

Q: Find the maximum and minimum values of y=x3+8x-0.4 Values should be exact. Do not round off.

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Q: Use the 3 point method or otherwise to sketch the graph of y=2x

A: We can sketch the  graph of y=2x By inserting the values x=0,1,2 Then we get values of y  for…

Q: State the vertex of the quadratic relation by completing the square, graph, and state the domain and…

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Q: Which points on the graph of y = 4 - x2 are closest to the point (0,2)? Ans. and

A: We will use Lagranges multiplier to find nearest points on graph

Q: Determine the concavity of the graphs of y^2=x and y=x^3

A: We have to determine the convexity of the graphs of y2 = x and y = x3 in between the points of their…

Q: Identify and sketch the graph of y = x² + 1 in R³.

A: Any point on the three dimensional coordinate system R3 can be represented by the point: x, y, z. A…

Q: Given the function, f (x) -2x² +6x- 4, answer the followi a) Find the vertex (enter it as an ordered…

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Q: Find the points of intersection of the graphs of the equations.                            x2 + y2 =…

A: From equation (2), we have

Q: Find the vertex. Give the range of the parabola in interval notation. y=x2-4x-7

A: To find the vertex of the parabola, we use the formula where (h, k) is the vertex of the parabola.…

Q: Determine whether the graphs of the two are parallel.  y+5=4x 3x-y=-5

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Q: what would the interpret for the solution for the graphed systerm?

A: The point at which the lines intersect is the intersection point.

Q: What is the domain of the quadratic graph?

A: as we can see, here function is continuous on -∞ , ∞

Q: What are the steps to graph (x3+2x2+x)  /  (2x2+x-1)

A: The given expression is

Q: If (-2,b) is a point on the graph of 2x+3y=2 ,what is b?

A: x,y=-2, b2x+3y=2

Q: (b) Find the number of points of intersection of the graph of y = = -x + 6x -(a + 9) and the x-axis.

A: It is given that the equation of the parabola is y=-x2+6x+a-9. We have to find the number of points…

Q: 4- Graph the function: |3x2 + бх — 24 x* + 4x – 5 -

A: See the attachment

Q: The graphs of f(x) = −4x2 − 10x + 7 and g(x) = 12x2 + 30x + 1 have the same axis of…

A: The graphs of f(x) = −4x2 − 10x + 7 and g(x) = 12x2 + 30x + 1 have the same axis of…

Q: Use the guidelines of the section to make a complete graph of ƒ. ƒ(x) = x - 3x2/3

A: Given function is fx=x-3x23.

Q: Find all points of intersection of the graphs of x2 − y = 3 and x − y = 1.

A: Definition used -         Solution of equations using graph -       We graph both equations on the…

Q: Sketch the set of points such that r2 12. Choose the correct graph below.

A: follow next step

Q: What is the piece-wise equation and domain for the 1t section of the graph? f(x)

A: NOTE: Refresh your page if you can't see any equations. . for the first part, the x-intercept is…

Q: Use the crossing- graphs method to solve the equation below. 3^x + x = 2^x +3

A: We graph y= 3x+x and y=2x+3 using a graphing calculator.

Q: Is the graph of r(x)=4x3−2x2+9x−2 concave up or down at the point with x-coordinate −1?

A: Given          r(x) = 4 x³ - 2x² + 9x - 2 For checking concave up or down we have to differentiate…

Q: Find the relative minimum point, maximum point, point of inflection and Sketch the graph of the…

A: Here, we need to find the relative minimum point, maximum point, point of inflection of the function…

Q: What is the relation of the graph of y= x² + 9x + 14 to a real-life situation – Area, Business, or…

A: Problem: You are an engineer building a suspension bridge. Your boss asked you to develop an…

Q: Find the maximum and minimum points and point of inflection of y = x* - 24x2 + 75.

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Q: Sketch the graph of y = x 2 + 4x + 6 by plotting the minimum point, the y-intercept, and one other…

A: Since the leading coefficient is 1, which is positive. So this parabola will have its minimum value…

Q: Explain the effect that the constant a has on the graph of y = ax². Be sure to consider a 0.

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

Q: Identify the vertex, the axis os symmetry, the maximum or minimum value, and the range of the…

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Q: The functions f(x) = −(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the…

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Q: How would you graph x is greater than or equal to 11

A: The given expression is,

Q: Suppose the graph of y = 5x + 7x – 2 is stretched horizontally by a factor of 4. The equation of the…

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Q: A farmer wants to fence a rectangular pasture for his chickens with his 100m of fences. By graphing…

A: we will find function to be maximize

Q: 9. If you were to graph f (x) = 2x2 + 4x – 6 , what would the coordinates of the vertex be? What…

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Q: If (2, b) is a point on the graph of y = x2 + 3x, what is b?

A: We have to find the value of b if point 2, b is lying on the graph of y=x2+3x. We know that if any…

Q: The absolute minimum of f(x) = 20x² – x+1 is Select one: -79 a. C-00 d.

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Q: y> -3x- 3

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Q: Here is a graph of x^2-2x-15=0   Where are the solutions in this graph? Describe their location on…

A: We have given a graph of x^2-2x-15=0 We have to find the solutions of this graph

Q: Is the graph of r(x) = -8x3 – 7x² + 2x +3 concave up or down at the point with r-coordinate –2?…

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Q: Given the following inequalities, choose only one then graph it manually and explain how it is was…

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Q: Find all points of intersection of the graphs of x2 − y = 3 and x − y = 1

A: To find the points of intersection, we solve both equations.

Q: Explain why the vertex is important when you are trying to find either the maximum y-value or the…

A: Every quadratic equation represents a parabola.

Q: Pick one of the two problems. Find the x-intercepts, vertex, determine if the vertex is a maximum or…

A: y = -(x-5)(x+1) X-INTERCEPTS (−1,0) ,(5,0) Y-INTERCEPTS (0,5) LOCAL MAXIMA (x,f(x))=(2,9)

Q: Give the function y = x2 + 8x – 9, state - whether the vertex represents a maximum or a minimum…

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Q: Graph the equation. Include the coordinates of any local extreme points and inflection points. y=…

A: Given the functiony=2x3+15x2+24x