Unit 8, Lesson 3
Solving Quadratic Equations by Reasoning
Algebra 1
Practice
Problem 1
Consider the equation \(x^2=9\).
- Show that 3, -3, \(\sqrt{9}\), and \(\text-\sqrt{9}\) are each a solution to the equation.
- Show that 9 and \(\sqrt{3}\) are each not a solution to the equation.
Problem 2
Solve \((x-1)^2 = 16\). Explain or show your reasoning.
Problem 3
Here is one way to solve the equation \(\frac59 y^2 = 5\). Explain what is done in each step.
\(\begin{align}\frac59y^2 &= 5 &\quad &\text{Original equation}\\5y^2&=45 &\quad &\text{Step 1} \\\\y^2&=9 &\quad& \text{Step 2} \\\\y=3 \qquad &\text{or} \qquad y=\text-3 &\quad& \text{Step 3} \end{align}\)