Please help
Use the function f(x) to answer the questions.

f(x) = −16x2 + 24x + 16

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)

Step-by-step explanation:

PART A

x-intercept happens when the graph pass through x-axis or when the coordinate y is equal to zero.

5x² + 2x - 3 = f(x)

5x² + 2x - 3 = y

5x² + 2x - 3 = 0

factorize

5x² + 2x - 3 = 0

(5x - 3)(x + 1) = 0

x = 3/5 or x = -1

There are two x-intercepts, those are 3/5 and -1

PART B

When the coefficient of x² is positive, the parabola has minimum vertex.

When the coefficient of x² is negative, the parabola has maximum vertex.

The coefficient of x² is 5, so the parabola has minimum vertex.

x of vertex =

x = -b/(2a)

x = -2/(2 × 5)

x = -2/10

x = -0.2

y of vertex

y = 5x² + 2x - 3

y = 5(-0.2)² + 2(-0.2) - 3

y = 0.2 - 0.4 - 3

y = -3.2

The vertex is (-0.2, -3.2)

PART C

First, define the x-intercept.

x = 3/5 = 0.6and

x = -1

Second, define the axis of symmetry

x = -b/(2a)

x = -2/(2 × 5)

x = -2/10

x = -0.2

Third, determine the vertex

The vertex is (-0.2, -3.2)

Put the x-intercept, axis of symmetry, and the vertex on cartesian plane. After that, draw the parabola.

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