Chapter 3, Problem 6CT

Determine the quadratic function for the given graph.

To determine

To find: The quadratic function of the given graph.

Answer to Problem 6CT

Solution:

The equation of the given parabola is $y=2{(x-1)}^2-32$.

Explanation of Solution

Given:

The given graph is

Formula used:

A parabola can be written in the form of a quadratic equation as $y=a{(x-h)}^2+k$, where $(h,k)$ is the vertex of the equation.

Calculation:

From the given parabola, we can see that the vertex of the parabola is at $(1,-32)$.

Thus, the equation of the parabola can be written as

$y=a{(x-1)}^2-32$

Now, we need to find the value of $a$.

We can see that $(0,-30)$ is a point on the parabola, on substituting the point in the above equation, we get

$-30=a{\left(0-1\right)}^2-32$

$\Rightarrow a=-30+32$

$\Rightarrow a=2$

Thus, the parabola is

$y=2{(x-1)}^2-32$