Lesson 15

Vertex Form

Let’s find out about the vertex form.

Select all of the quadratic expressions in vertex form.

$(x-2)^2 + 1$

$x^2 - 4$

$x(x+1)$

$(x+3)^2$

$(x-4)^2 + 6$

Here are two equations. One defines function $m$ and the other defines function $p$ .

$m(x)=x(x+6)$

$p(x)=(x+3)^2-9$

Show that the expressions defining $m$ and $p$ are equivalent.
What is the vertex of the graph of $m$ ? Explain how you know.
What are the $x$ -intercepts of the graph of $p$ ? Explain how you know.

Which equation is represented by the graph?

Parabola. Opens down. Vertex = -3 comma -1.

$y=(x-1)^2+3$

$y=(x-3)^2+1$

$y=\text-(x+3)^2-1$

$y=\text-(x-3)^2+1$

For each equation, write the coordinates of the vertex of the graph that represents the equation.

$y=(x-3)^2 + 5$
$y=(x+7)^2 + 3$
$y=(x-4)^2$
$y=x^2 - 1$
$y=2(x+1)^2-5$
$y=\text-2(x+1)^2-5$

For each function, write the coordinates of the vertex of its graph and tell whether the graph opens up or down.

function	coordinates of vertex	graph opens up or down?
$f(x)=(x-4)^2-5$
$g(x)=\text-x^2+5$
$h(x)=2(x+1)^2-4$

Here is a graph that represents $y = x^2$ .

Describe what would happen to the graph if the original equation were modified as follows:
1. $y=\text-x^2$
2. $y=3x^2$
3. $y=x^2 + 6$
Sketch the graph of the equation $y=\text-3x^2 + 6$ on the same coordinate plane as $y=x^2$ .

(From Unit 6, Lesson 12.)

Noah is going to put $2,000 in a savings account. He plans on putting the money in an account and leaving it there for 5 years. He can put the money in an account that pays 1% interest monthly, an account that pays 6% interest every six months, or an account that pays 12% interest annually.

Which account will give him the most money in his account at the end of the 5 years?

(From Unit 5, Lesson 16.)

Here are four graphs. Match each graph with a quadratic equation that it represents.