Chapter 4.3, Problem 5LC

Solution

To State: The explanation for the given quadratic functions attains the greatest values.

Find the equation that passing through the points and substitute a random value to both

function and then observe which equation attains the maximum value.

Given:

Explain how to determine which of the quadratic functions attains the greatest values.

Explanation:

Explanation for to find which quadratic functions attains the greatest values:

Take the first three points from the equation and use the standard form of a quadratic equation $y=a{x}^2+bx+c$ as the starting point for finding the equation through the three points.

Create a system of equations by substituting the $x$ and $y$ values of each point into the standard formula of a quadratic equation to create the three-equation system.

Then solve the system of equations to find the values of $a,b$ and $c$ .

Substitute the actual values of $a,b$ and $c$ into the formula for a quadratic equation to find the resulting equation.

Then substitute some random similar value to both of the given quadratic functions and observe which equation attains the greater value.