Question

HELP PLS MANY POINTS Use the function f(x) to answer the questions: f(x) = 4x2 + 8x − 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. (5 point

Answer 1

Answer:

see below

Step-by-step explanation:

f(x) = 4x^2 + 8x − 5

To find the x intercepts set y = 0

0 =4x^2 + 8x − 5

Factor

0=(2x-1)(2x+5)

Using the zero product property

2x-1 =0     2x+5 =0

2x=1            2x = -5

x = 1/2           x = -5/2

The x intercepts are ( 1/2 ,0)   and ( -5/2,0)

Rewriting in vertex form by completing the square

4 ( x^2 + 2x) -5

4 ( x^2+2x +1) -4*1 -5

4 ( x+1) ^2 -9

Vertex form is

a( x-h) ^2 +k  where ( h,k) is the vertex

The vertex is ( -1,-9)

We know it opens upwards since a > 0

Plot the vertex and the x intercepts

The graph is symmetric on  based on the vertex