# Lesson 24

Quadratic Situations

- 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.

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

### 24.2: Diego’s Plant

- 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.

- Write your own true statement about Diego’s plant.

### 24.3: Making the Grades

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 \(T(h) = 6h + 76\).

Here’s a graph of both functions:

- Which graph represents Jada’s quiz grade after \(h\) hours of studying?
- What do the \(y\)-intercepts of the lines mean in this situation?
- Find the coordinates of the \(y\)-intercepts.
- The 2 lines intersect at a point. What does that point represent in this situation?
- Find the coordinates of the intersection point. Explain or show your reasoning.