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100 Points!
Use the function f(x) to answer the questions:


f(x) = 4x2 − 7x − 15


Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)


Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)


Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Respuesta :

upandover

Part A: x = -5/4, 3 || (-5/4, 0) (3, 0)

To find the x-intercepts, we need to know where y is equal to 0. So, we will set the function equal to 0 and solve for x.

4x^2 - 7x - 15 = 0

4 x 15 = 60 || -12 x 5 = 60 || -12 + 5 = -7

4x^2 - 12x + 5x - 15 = 0

4x(x - 3) + 5(x - 3) = 0

(4x + 5)(x - 3) = 0

4x + 5 = 0

x = -5/4

x - 3 = 0

x = 3

Part B: minimum, (7/8, -289/16)

The vertex of the graph will be a minimum. This is because the parabola is positive, meaning that it opens to the top.

To find the coordinates of the parabola, we start with the x-coordinate. The x-coordinate can be found using the equation -b/2a.

b = -7

a = 4

x = -(-7) / 2(4) = 7/8

Now that we know the x-value, we can plug it into the function and solve for the y-value.

y = 4(7/8)^2 - 7(7/8) - 15

y = 4(49/64) - 49/8 - 15

y = 196/64 - 392/64 - 960/64

y = -1156/64 = -289/16 = -18 1/16

Part C:

First, start by graphing the vertex. Then, use the x-intercepts and graph those. At this point we should have three points in a sort of triangle shape. If we did it right, each of the x-values will be an equal distance from the vertex. After we have those points graphed, it is time to draw in the parabola. Knowing that the parabola is positive, we draw in a U shape that passes through each of the three points and opens toward the top of the coordinate grid.

Hope this helps!

sparklycookie2017

Answer:

Give the other guy brainliest

Step-by-step explanation:

Part A: The x-intercepts are (-5/4, 0) and (3, 0)

0=4x^2-7x-15

0=4x^2-12x+5x-15

0=4x(x-3)+5(x-3)

0=(4x+5)(x-3)

Basic math:

x=-5/4

x=3

Part B: The vertex is going to be minimum because if a>0, then the parabola opens up and it is a minimum (a as in ax^2+bx+c).

In order to find the vertex's coordinates, we can use -b/2a. In the equation, b=-7, and a=4. The formula would look like or 7/8. We now know the x coordinate. We can use that to find the y value.

y=4(7/8)^2-7(7/8)-15=y=18  =-18.0625=289/16

Part C: Graph the x-intercepts found in part A, then graph the vertex found in part B. Then graph a U shape that opens up going through all the points to make the parabola. Because it is positive, the U will face up, not down.

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