Unit 5, Lesson 17
Applying the Quadratic Formula (Part 1)
Integrated Math 2
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Select all the equations that have 2 solutions.
\((x + 3)^2 = 9\)
\((x - 5)^2 = \text- 5\)
\((x + 2)^2-6 = 0\)
\((x - 9)^2+25 = 0\)
\((x + 10)^2 = 1\)
\((x - 8)^2 = 0\)
\(5=(x+1)(x+1)\)
A frog jumps in the air. The height, in inches, of the frog is modeled by the function \(h(t) = 60t-75t^2\), where \(t\) is the time after it jumped, measured in seconds.
Solve \(60t - 75t^2 = 0\). What do the solutions tell us about the jumping frog?
A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation \(f(t) = 4 + 12t - 16t^2\), where \(t\) is measured in seconds since the ball was thrown.
Rewrite each quadratic expression in standard form.
Find the missing expression in parentheses so that each pair of quadratic expressions is equivalent. Show that your expression meets this requirement.
Consider the equation \(4x^2 - 4x -15 = 0\).
Evaluate each expression using the values of \(a\), \(b\), and \(c\).
\(\text- b\)
\(b^2\)
\(4ac\)
\(b^2 - 4ac\)
\(\sqrt{b^2 - 4ac}\)
\(\text- b \pm \sqrt{b^2 - 4ac}\)
\(2a\)
\(\dfrac{\text- b \pm \sqrt{b^2 - 4ac}}{2a}\)
Without graphing, describe how adding \(16x\) to \(\text-x^2\) would change each feature of the graph of \(y = \text-x^2\). (If you get stuck, consider writing the expression in factored form.)