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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

2. Standard Form of a Quadratic Function

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Exercise 64 Page 208

The vertex form of a quadratic function is $y = a (x - h)^{2} + k .$

Vertex: $(3, - 2)$
Axis of Symmetry: $x = 3$
Minimum Value: $(3, - 2)$
Domain: All real numbers.
Range: $y \geq - 2$

Practice makes perfect

We want to identify the vertex, axis of symmetry, maximum or minimum value, domain, and range of the given quadratic function. To do so, we will first express it in vertex form,

y = a (x - h)^{2} + k,

where

a,

h,

and

k

are either positive or negative constants.

y = \frac{1}{2} (x - 3)^{2} - 2 ⇕ y = \frac{1}{2} (x - 3)^{2} + (- 2)

It is important to note that we do not need to graph the parabola to identify the desired information. Let's compare the general formula for the vertex form to our equation.

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Subchapter links

Lesson Check p.206

Practice and Problem-Solving Exercises p.206-208

Standardized Test Prep p.208

Mixed Review p.208