Unit 8, Lesson 18
Applying the Quadratic Formula (Part 2)
Algebra 1
Practice
Problem 1
Mai and Jada both solve the equation \(2x^2 - 7x = 15\) using the quadratic formula but find different solutions.
Mai writes:
\(\displaystyle \begin{align} x &= \frac{\text- 7 \pm \sqrt{7^2 - 4(2)(\text-15)}}{2(2)}\\ x &= \frac{\text- 7 \pm \sqrt{49 - (\text- 120)}}{4}\\ x &= \frac{\text- 7 \pm \sqrt{169}}{4}\\ x &= \frac{\text- 7 \pm 13}{4}\\ x &= \text- 5 \quad \text{ or } \quad x = \frac32\\ \end{align}\\\)
Jada writes:
\(\displaystyle \begin{align} x &= \frac{\text- (\text- 7) \pm \sqrt{\text- 7^2 - 4(2)(\text-15)}}{2(2)}\\ x &= \frac{7 \pm \sqrt{\text- 49 - (\text- 120)}}{4}\\ x &= \frac{7 \pm \sqrt{71} }{4}\\ \end{align}\\\)
- If this equation is written in standard form, \(ax^2+bx+c=0\), what are the values of \(a, b\), and \(c\)?
- Do you agree with either of them? Explain your reasoning.
Problem 2
The equation \(h(t)=\text-16t^2+80t+64\) represents the height, in feet, of a potato \(t\) seconds after it was launched from a mechanical device.
- Write an equation that would allow us to find the time the potato hits the ground.
- Solve the equation without graphing. Show your reasoning.