# Lesson 12

Graphing the Standard Form (Part 1)

- Let’s see how the numbers in expressions like \(\text-3x^2+4\) affect their graph.

### Problem 1

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

### Problem 2

The two equations \(y=(x+2)(x+3)\) and \(y=x^2 + 5x + 6\) are equivalent.

- Which equation helps find the \(x\)-intercepts most efficiently?
- Which equation helps find the \(y\)-intercept most efficiently?

### Problem 3

Here is a graph that represents \(y = x^2\).

On the same coordinate plane, sketch and label the graph that represents each equation:

- \(y = x^2 -4\)
- \(y = \text-x^2 + 5\)

### Problem 4

Select **all** equations whose graphs have a \(y\)-intercept with a positive \(y\)-coordinate.

\(y=x^2 + 3x - 2\)

\(y=x^2 - 10x\)

\(y=(x-1)^2\)

\(y=5x^2-3x-5\)

\(y=(x+1)(x+2)\)

### Problem 5

- Describe how the graph of \(A(x)=|x|\) has to be shifted to match the given graph.
- Write an equation for the function represented by the graph.

### Problem 6

Here is a graph of the function \(g\) given by \(g(x) = a \boldcdot b^x\).

What can you say about the value of \(b\)? Explain how you know.

### Problem 7

- What are the \(x\)-intercepts of the graph that represents \(y = (x+1)(x+5)\)? Explain how you know.
- What is the \(x\)-coordinate of the vertex of the graph that represents \(y = (x+1)(x+5)\)? Explain how you know.
- Find the \(y\)-coordinate of the vertex. Show your reasoning.
- Sketch a graph of \(y = (x+1)(x+5)\).

### Problem 8

Determine the \(x\)-intercepts, the vertex, and the \(y\)-intercept of the graph of each equation.

equation | \(x\)-intercepts | vertex | \(y\)-intercept |
---|---|---|---|

\(y=(x-5)(x-3)\) | |||

\(y=2x(8-x)\) |

### Problem 9

Equal amounts of money were invested in stock A and stock B. In the first year, stock A increased in value by 20%, and stock B decreased by 20%. In the second year, stock A decreased in value by 20%, and stock B increased by 20%.

Was one stock a better investment than the other? Explain your reasoning.