Range of a quadratic equation

Introduction

In this article, we'll practice finding the range of

y

-values of quadratic equations in vertex form, such as

y = - 2 (x + 3)^{2} + 7

. To do this article, you should already know how to graph parabolas.

Let's breakdown how to find the range of

y = - 5 (x - 2)^{2} + 3

without seeing the graph.

Step 1: Find the

y

-coordinate of the vertex of the parabola.

Step 2: Does the parabola open up or down?

Step 3: Is the

y

-coordinate of the vertex a minimum or a maximum?

What is the range of the parabola's $y$ ‍-values?
Write an inequality in terms of $y$ ‍.

What is the range of possible $y$ ‍-values for $y = \frac{1}{2} (x - 3)^{2} + 2$ ‍?
Write an inequality in terms of $y$ ‍.

What is the range of possible $y$ ‍-values for $y = - 7 (x + 3)^{2} - 6$ ‍?
Write an inequality in terms of $y$ ‍.

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