# Lesson 24

• Let’s work with situations and quadratic equations.

### 24.1: Growing Plants

Plant A’s height over time is represented by $$y=\frac{1}{2}x+4$$. Plant B’s height is $$y=\frac{1}{3}x+3$$ for which $$x$$ represents the number of weeks since the plants were found, and $$y$$ represents the height in inches.

1. Which graph goes with which equation? How do you know?
2. What is a pair of values that works for Plant A but not B? What does it represent?
3. What is a pair of values that works for Plant B but not A? What does it represent?
4. What is a pair of values that works for both plants? What does it represent?

### 24.2: Diego’s Plant

1. The height, in centimeters, of Diego’s plant is represented by the equation $$p(t) = \text{-}0.5(t-10)^2+58$$ where $$t$$ represents the number of weeks since Diego has started nurturing the plant. Determine if each statement is true or false. Explain your reasoning.
• Diego’s plant shrinks each week.
• Diego’s plant is 8 cm tall when he starts to nurture it.
• Diego’s plant grows to be 58 cm tall.
• The plant shrinks 4 weeks after Diego begins to nurture it.

Jada’s quiz grade after $$h$$ hours of studying is given by the equation $$Q(h) = 10h + 70$$. Her test grade after $$h$$ hours of studying is given by the equation $$T(h) = 6h + 76$$.
1. Which graph represents Jada’s quiz grade after $$h$$ hours of studying?
2. What do the $$y$$-intercepts of the lines mean in this situation?
3. Find the coordinates of the $$y$$-intercepts.