Question

What are the vertex and x-intercepts of the graph of y=(x-4)(x+2)?

Answer 1

Answer:

A. x-intercepts: (4,0),(-2,0)

C. Vertex: (1,-9)

Step-by-step explanation:

We have been given factored form of a quadratic equation $y=(x-4)(x+2)$. We are asked to find vertex and x-intercepts of our given equation.

We know that x-intercepts of a graph are those points at which graph touches or crosses x-axis and y-coordinates of x-intercepts are always zero.

So we will substitute $y=0$ in our given equation to find the x-intercepts.

$0=(x-4)(x+2)$

$(x-4)=0\text{ or }(x+2)=0$

$x-4+4=0+4\text{ or }x+2-2=0-2$

$x=4\text{ or }x=-2$

Since y-coordinates of x-intercepts will be 0, therefore, x-intercepts of the graph will be (4,0), (-2,0) and option A is the correct choice.

To find the vertex of the parabola, we will expand our given expression using FOIL.

$(x-4)(x+2)$

$x*x+x*2-4*x-4*2$

$x^2+2x-4x-8$

$x^2-2x-8$

We will use formula $\frac{-b}{2a}$ to find the x-coordinate of vertex of parabola, where, a and b represents the coefficient of $x^2\text{ and }x$ respectively.

$\text{x-coordinate of vertex}=\frac{-(-2)}{2*1}$

$\text{x-coordinate of vertex}=\frac{2}{2}=1$

Now we will substitute $x=1$ in the expression to find the y-coordinate of parabola.

$\text{y-coordinate of vertex}=1^2-2*1-8$

$\text{y-coordinate of vertex}=1-2-8$

$\text{y-coordinate of vertex}=-9$

Therefore, the vertex of parabola will be at point (1,-9) and option C is the correct choice.