Question

Draw the graph of the polynomial $f\left(x\right)=x^2-2x-8$

Answer 1

Given,

$f\left(x\right)=x^2-2x-8$

to find the vertex, we know,

$x=-\frac{b}{2a}=-\frac{-2}{2\times 1}=1$

to find y coordinate, substitute the value of x in equation.

$(1{)}^2-2(1)-8=1-2-8=9$

The vertex is $(1,9)$

Now, x intercepts,

$x^2-2x-8=0$

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

$x=-2,4$

The x intercepts are $(-2,0),(4,0)$

To find the y intercept, substitute $x=0$ in given equation,

$0^2-2\left(0\right)-8=-8$

The y intercept is $(0,-8)$

Thus it is an upward facing parabola, touching x and y axis at $(2,-8),(-1,-5),(3,-5)$