Question

Quation, In factored form, of the quadratic function shown in the graph? (-3,0), (3,0)

Answer 1

Given: The graph of a quadratic equation as shown

To Determine: The equation of the graph

Solution

Let us determine the zeros

The zeros of the equation is given as the points where the curve cuts the x-axis

`\begin{gathered} x=-3 \\ x+3=0 \\ x=2 \\ x-2=0 \\ f(x)=a(x-2)(x+3) \end{gathered}`

The y-intercept is

`\begin{gathered} y-intercept \\ (0,-6) \end{gathered}`

Substitute the coordinate of the y-axis to get the value of a

So,

`\begin{gathered} -6=a(0-2)(0+3) \\ -6=a(-2)(3) \\ -6=-6a \\ a=(-6)/(-6) \\ a=1 \end{gathered}`

Hence the equation of the graph is

f(x) = 1(x + 3)(x -2)