Lesson 13
Graphing the Standard Form (Part 2)
- Let’s change some other parts of a quadratic expression and see how they affect the graph.
Problem 1
Here are four graphs. Match each graph with the quadratic equation that it represents.
Graph A
Graph B
Graph C
Graph D
Problem 2
Complete the table without graphing the equations.
| equation | \(x \)-intercepts | \(x \)-coordinate of the vertex |
|---|---|---|
| \(y=x^2+12x\) | ||
| \(y=x^2-3x\) | ||
| \(y=\text-x^2+16x\) | ||
| \(y=\text-x^2-24x\) |
Problem 3
Here is a graph that represents \(y = x^2\).
- Describe what would happen to the graph if the original equation were changed to \(y=x^2-6x\). Predict the \(x\)- and \(y\)-intercepts of the graph and the quadrant where the vertex is located.
- Sketch the graph of the equation \(y=x^2 -6x\) on the same coordinate plane as \(y=x^2\).
Problem 4
Select all equations whose graph opens upward.
\(y=\text-x^2 + 9x\)
\(y=10x-5x^2\)
\(y=(2x-1)^2\)
\(y=(1-x)(2+x)\)
\(y=x^2-8x-7\)
Problem 5
Technology required. Write an equation for a function that can be represented by each given graph. Then, use graphing technology to check each equation you wrote.
Graph 1
Graph 2
Graph 3
Problem 6
Match each quadratic expression that is written as a product with an equivalent expression that is expanded.
Problem 7
When buying a home, many mortgage companies require a down payment of 20% of the price of the house. What is the down payment on a $125,000 home?
Problem 8
A bank loans $4,000 to a customer at a \(9\frac{1}{2}\%\) annual interest rate.
Write an expression to represent how much the customer will owe, in dollars, after 5 years without payment.