Question

SERIOUS ANSWERS ONLY WILL GIVE BRAINLIEST

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 points)

Answer 1

Hello,

Part A:

$f(x)=4x^2+8x-5\\=4(x^2+2x)-5\\=4(x^2+2x+1-1)-5\\=4(x+1)^2-9\\=(2(x+1)-3)(2(x+1)+3)\\=(2x-1)(2x+5)\\x-intercepts\ are\ x=\frac{1}{2} \ and\ x=-\frac{5}{2}$

Part B:

x² coefficient is 4 >0 thus a minimun

as y=4(x+1)²-9 : vertex is (-1,-9)

Proof: see picture

Sorry for Part c: I don't know

In France, we make an array of (x,f(x)) and then plot the severals points.