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

Question

Use the function f(x) to answer the questions:

f(x) = 2x² − 3x − 5

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. (

Answer 1

A: Let f(x) = 0 and solve for x to get the x intercepts.

2x² -3x -5 =0 Factor to get (2x -5) (x + 1) =0 then

2x - 5 = 0 and x = 2.5 x + 1 = 0 and x = -1 These are the x intercepts.

B: As the coefficient of the x^2 term is positive, the parabola open up, and the vertex is a minimum. The coordinates of the parabola are given by -b/2a, f( -b/2a) where a and b represent the coefficients of a parabola in the standard form ax^2 + bx +c = 0. In this case a = 2, be = -3, c = -5. So -b/2a = 3 / 4 f( -b/2a) = 2 * (3/4)^2 -3 * (3/4) - 5 = -6.125. The coordinates of the vertex are (3/4, -6.125)

C: To graph this function, first establish where the vertex will be from the coordinates found. Next plot the position of the x intercepts. You know it opens up, so you would draw it so the vertex is a minimum. You could also get the y intercept by letting x = 0, which gives -5 for the y intercept. This should give you a rough idea of what the graph looks like.

Answer 2

Hi Luna K

For

f(x) = 2x²-3x -5

For Part A

Set f(x) = 0

Factor the Quadratic

Set the factors = 0

Solve each factor for x to find your x intercepts

For Part B

You need to use the coefficients in your Quadratic

List them

a = 2 , b = -3 and c = -5

Since a is positive, your parabola opens up

Find the x coordinate of the vertex it is -b/2a

One you get the x coordinate, plug it into to your Quadratic to get f(x) your y coordinate of the vertex

For Part C

You can plot the vertex, both x intercepts on a coordinate grid

Give the information above a try, you can also look up the Standard Form Equation of a Parabola in your text or online to confirm the information above.