Question

Could you please answer these and show me how to get to the answers?

Answer 1

Given the function:

$y=x^2-4x-5$

- Factor to find the x-intercept:

Factor and equal to zero for Vertexeach factor.

$x^2-4x-5=(x-5)(x+1)$

So:

$\begin{gathered} x-5=0 \\ x=5 \\ \text{and} \\ x+1=0 \\ x=-1 \end{gathered}$

a) The vertex of a parabola is:

$x=-\frac{b}{2a}$

The parameters of the parabola are:

a = 1, b = -4 and c = -5

$x=-\frac{-4}{2(1)}=\frac{4}{2}=2$

We find y:

$y=(2)^2-4(2)-5=4-8-5=-9$

Therefore the vertex of the parabola is: (2, -9)

b) x-intercepts are: (5,0) and (-1,0)

c) Vertex: (2, -9)

d) Graph:

- Table:

x y

-1 0

0 -5

1 -8

2 -9

3 -8

4 -5

5 0

6 7