Lesson 10

A quadratic function $f$ is defined by $f(x)=(x-7)(x+3)$.

1. Without graphing, identify the $x$-intercepts of the graph of $f$. Explain how you know.
2. Expand $(x-7)(x+3)$ and use the expanded form to identify the $y$-intercept of the graph of $f$.

What are the $x$-intercepts of the graph of the function defined by $(x-2)(2x+1)$?

$(2,0)$ and $(\text-1,0)$

$(2,0)$ and $\left(\text-\frac12,0\right)$

$(\text-2,0)$ and $(1,0)$

$(\text-2,0)$ and $(\frac12,0)$

$(x+3)(x+1)$

$(x+3)(x-1)$

$(x-3)(x+1)$

$(x-3)(x-1)$

1. What is the $y$-intercept of the graph of the equation $y = x^2 - 5x + 4$?
2. An equivalent way to write this equation is $y = (x-4)(x-1)$. What are the $x$-intercepts of this equation’s graph?

Noah said that if we graph $y=(x-1)(x+6)$, the $x$-intercepts will be at $(1,0)$ and $(\text-6,0)$. Explain how you can determine, without graphing, whether Noah is correct.

A company sells a video game. If the price of the game in dollars is $p$ the company estimates that it will sell $20,\!000 - 500p$ games.

Which expression represents the revenue in dollars from selling games if the game is priced at $p$ dollars?

$(20,\!000 - 500p) + p$

$(20,\!000 - 500p) - p$

$\dfrac{20,000 - 500p}{p}$

$(20,\!000 - 500p) \boldcdot p$

Write each quadratic expression in standard form. Draw a diagram if needed.

1. $(x-3)(x-6)$
2. $(x-4)^2$
3. $(2x+3)(x-4)$
4. $(4x-1)(3x-7)$

Consider the expression $(5+x)(6-x)$.

1. Is the expression equivalent to $x^2+x+30$? Explain how you know.
2. Is the expression $30+x-x^2$ in standard form? Explain how you know.

$g(x) = 25 \boldcdot 3^x$

$g(x) = 50 \boldcdot (1.5)^x$

$g(x) = 100 \boldcdot 3^x$

$g(x) = 200 \boldcdot (1.5)^x$