Lesson 11
Graphing from the Factored Form
- Let’s graph some quadratic functions in factored form.
Problem 1
Select all true statements about the graph that represents \(y=2x(x-11)\).
Its \(x\)-intercepts are at \((\text-2,0)\) and \((11,0)\).
Its \(x\)-intercepts are at \((0,0)\) and \((11,0)\).
Its \(x\)-intercepts are at \((2,0)\) and \((\text-11,0)\).
It has only one \(x\)-intercept.
The \(x\)-coordinate of its vertex is -4.5.
The \(x\)-coordinate of its vertex is 11.
The \(x\)-coordinate of its vertex is 4.5.
The \(x\)-coordinate of its vertex is 5.5.
Problem 2
Select all equations whose graphs have a vertex with \(x\)-coordinate 2.
\(y=(x-2)(x-4)\)
\(y=(x-2)(x+2)\)
\(y=(x-1)(x-3)\)
\(y=x(x+4)\)
\(y=x(x-4)\)
Problem 3
Determine the \(x\)-intercepts and the \(x\)-coordinate of the vertex of the graph that represents each equation.
| equation | \(x \)-intercepts | \(x\)-coordinate of the vertex |
|---|---|---|
| \(y=x(x-2)\) | ||
| \(y=(x-4)(x+5)\) | ||
| \(y= \text-5x (3-x)\) |
Problem 4
Which one is the graph of the equation \(y=(x-3)(x+5)\)?
Graph A
Graph B
Graph C
Graph D
Graph A
Graph B
Graph C
Graph D
Problem 5
- What are the \(x\)-intercepts of the graph of \(y=(x-2)(x-4)\)?
- Find the coordinates of another point on the graph. Show your reasoning.
- Sketch a graph of the equation \(y = (x-2)(x-4)\).
Problem 6
A company sells calculators. If the price of the calculator in dollars is \(p\), the company estimates that it will sell \(10,\!000-120p\) calculators.
Write an expression that represents the revenue in dollars from selling calculators if a calculator is priced at \(p\) dollars.
Problem 7
Is \((s+t)^2\) equivalent to \(s^2+2st+t^2\)? Explain or show your reasoning.
Problem 8
Tyler is shopping for a truck. He found two trucks that he likes. One truck sells for $7,200. A slightly older truck sells for 15% less. How much does the older truck cost?
Problem 9
Here are graphs of two exponential functions, \(f\) and \(g\).
The function \(f\) is given by \(f(x) = 100 \boldcdot 2^x\) while \(g\) is given by \(g(x) = a \boldcdot b^x\).
Based on the graphs of the functions, what can you conclude about \(a\) and \(b\)?
Problem 10
Suppose \(G\) takes a student’s grade and gives a student’s name as the output. Explain why \(G\) is not a function.