What is the range of the function y= -3x² + 6x +4?

1 Answer
Aug 8, 2017

Solution 1.

The y value of the turning point will determine the range of the equation.

Use the formula x=-b/(2a) to find the x value of the turning point.

Substitute in the values from the equation;

x=(-(6)) / (2(-3))

x=1

Substitute x=1 into the original equation for the y value.

y=-3(1)^2 + 6(1) + 4

y=7

Since the a value of the quadratic is negative, the turning point of the parabola is a maximum. Meaning all y values less than 7 will fit the equation.

So the range is y≤ 7.

Solution 2.

You can find the range visually by graphing the parabola. The following graph is for the equation -3x^2 + 6x + 4

graph{-3x^2 + 6x + 4 [-16.92, 16.94, -8.47, 8.46]}

We can see that the maximum value of y is 7. Therefore, the range of the function is y≤ 7.