Use the function f(x) = 5x2 + 2x - 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and
Part C to draw the graph. (4 points)

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.

hope it helps you tbh google ;)

here the number -5 is all of the following except a rational number.

step-by-step explanation:

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.