Review of Linear and Quadratic Functions Exercises

Subsection 0.1 Review of Linear and Quadratic Functions Exercises

Write a linear function equation for each function given below.
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1. The function $q$ shown in the graph below.
  $The graph of $q(t)$ is a straight line with positive slope. It intersects the vertical axis at $q(0) = -4$ and crosses the horizontal axis near $t \approx 2\text{.}$ The function increases steadily as $t$ increases.$
  
  Figure 0.1.10. Graph of $q(t)\text{.}$
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2. The function $y$ shown in the graph below.
  $The graph of $y(x)$ is a straight line with negative slope. It intersects the vertical axis at $y(0) = 2$ and crosses the horizontal axis near $x \approx 1\text{.}$ The function decreases steadily as $x$ increases.$
  
  Figure 0.1.11. Graph of $y(x)\text{.}$
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3. The function $b$ shown in the table below.
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  Table 0.1.12.
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  $x$ $-2$ $-1$ 0 1 2
  
  $b(x)$ $-5$ $-1$ $3$ $7$ $11$
  
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4. The function $h$ shown in the table below.
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  Table 0.1.13.
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  $t$ $-2$ $-1$ 0 1 2
  
  $h(t)$ $-74$ $-62$ $-50$ $-38$ $-26$
  
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Giovanni is saving money to buy a PS5. He started saving with $145 (that he got for Christmas), and he is able to save $35 per week from his paycheck to put toward the PS5.
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1. Write an equation for $s(t)\text{,}$ the amount of savings Giovanni has $t$ weeks after he started saving.
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2. How much will Giovanni have saved after 6 weeks?
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3. How long will it take Giovanni to save enough money for a PS5 ($500)?
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A car rental company charges $40 for the first day of car rental, and $30 for each day after that.
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1. Write an equation for $c(d)\text{,}$ the total cost to rent a car for $d$ days.
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2. How much will it cost to rent a car for 15 days?
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3. For how many days did you rent a car if you paid $280?
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Solve each equation or inequality below.
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1. $\displaystyle 1-n+6n=6$
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2. $\displaystyle 3(1+5x)=78$
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3. $\displaystyle 6(-x-5)-2x=-78$
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4. $\displaystyle -2(-7n-11)=8(n-4)$
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5. $\displaystyle 3+10x > 33$
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6. $\displaystyle -7 \geq \frac{-10+a}{3}$
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7. $\displaystyle -2(5+5m) > -90$
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8. $\displaystyle 3+4r \leq 7(7r-6)$
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Use the graph of $z(x)$ below to answer the following questions.
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$The graph of $z(x)$ is an upward-opening parabola. The vertex is at $(10, -50)\text{,}$ which is the minimum point of the curve. The graph crosses the horizontal axis at two points, at $x = 3$ and $x = 17\text{,}$ and increases on both sides of the vertex.$

Figure 0.1.14. Graph of $z(x)\text{.}$
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1. What is the vertex of the graph of $z\text{?}$
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2. Write an equation for $z\text{.}$
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3. Solve $z(x)=50\text{.}$
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4. Solve $z(x) \geq 50\text{.}$
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5. Find the $x-$intercepts of $z\text{.}$
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6. Find the vertical intercept of $z\text{.}$
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7. What are the domain and range of $z\text{?}$
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Solve each equation below.
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1. $\displaystyle n^2+3n-28=0$
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2. $\displaystyle p^2=7p$
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3. $\displaystyle 3x^2-x-14=0$
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4. $\displaystyle r^2-20=-r$
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5. $\displaystyle 8x^2+3=64x+3$
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6. $\displaystyle 3b^2+1=4$
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7. $\displaystyle 12x^2-12=11x$
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8. $\displaystyle 6x^2-5=-7x$
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9. $\displaystyle n^3+n^2-2n=0$
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10. $\displaystyle a^4-6a^2-16=0$
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\(x\)	\(-2\)	\(-1\)	0	1	2
\(b(x)\)	\(-5\)	\(-1\)	\(3\)	\(7\)	\(11\)

\(t\)	\(-2\)	\(-1\)	0	1	2
\(h(t)\)	\(-74\)	\(-62\)	\(-50\)	\(-38\)	\(-26\)

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