Question

40 POINTS! Please HELP!!!Use the function f(x) to answer the questions:

f(x) = 5x^2 + 2x - 3
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 2: 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)

Answer 1

Explanation:

Eq.
`5x^2 + 2x - 3`

Part A:

1. Set the output value
`f(x)` (also known as "y" on a coordinate plane) = 0

2.
`5x^2 + 2x - 3` = 0

3. Factor using "ac" method. (5 x 3 = 15, what factors of 15 when added/subtracted = 2?)

• 
  `5x^2 + 5x - 3x - 3` = 0
• 5x(x + 1) - 3(x + 1) = 0
• (5x - 3)(x + 1) = 0

4. Use zero property.

• 5x - 3 = 0
• 5x = 3
• x = 3/5

OR

• x + 1 = 0
• x = - 1

5. These are the x-intercepts: (3/5, 0) and (- 1, 0)

Part B:

Vertex Formula: x = -b/2a

In a quadratic equation the base equation (standard form) is ax^2 + bx + c, where a is a non-zero constant, and b and c are real numbers.

(eq. 5x^2 + 2x - 3)

-2/2(5) = -2/10 = - 1/5 --> x-coordinate

plug (- 1/5) in for x to get - 16/5 as the y-coordinate.

VERTEX: (-1/5, - 16/5) ; minimum because "a" value is positive

Answer 2

Part A: (-1, 0), (0.6, 0)

Part B: Minimum, (-0.2, -3.2)

Part 2: We would find the 3 points: the 2 zeros and the vertex and we would be able to graph.

Explanation:

Easiest and fastest way to answer these questions is to graph the equation in a graphing calc.