(100 points & Brainliest!)

Use the function f(x) = 5x2 + 2x − 3 to answer the questions.

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

Part B: Describe the end behavior of the graph of f(x). Explain. (2 points)

Part C: 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: -1, and .6

Part B: As x approaches infinity, y approaches infinity. As x approaches negative infinity, y approaches infinity.

Part C:

1st I would graph the x intercepts (-1, 0) and (.6, 0)

2nd I would graph the y intercept (0, -3)

3rd. Draw the parabola that connects the dots

Step-by-step explanation:

The function factors into (x+1)(5x-3) so we know that the x intercepts are -1 and 3/5 (or .6).

The y intercept is -3, as determined by C

A) x = -1 , ⅗

B) open upwards

C) see below

Step-by-step explanation:

A) 5x² + 2x - 3 = 0

5x² + 5x - 3x - 3 = 0

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

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

x = -1, ⅗

B) it's a concave up. It will open upwards, both ends of the curve increasing/upwards

C) to sketch, we need

1) shape: concave up (part B)

2) x-intercepts: -1, ⅗ (part A)

3) y-intercept: -3

4) vertex

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