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#.