Quadratic Formula
Solve by the quadratic formula. List the solutions, separated by commas.
\[
3 x^{2}+1 x-10=0
\]
\[
x=
\]
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Solving by Factoring
$4 b^{2}+8 b+7=4$
Solve by Completing the Square
Solve the quadratic equation by completing the square.
\[
x^{2}-6 x-2=0
\]
First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
Form:
$(x+\square)^{2}=$
$(x-\square)^{2}=$
Solution:
\[
x=
\]
Finding the Perfect Square Trinomial
$y=(x+3)^{2}+2$
Finding the Quadratic Equation Given the Solution Set
Write a quadratic function $f$ whose zeros are 7 and -2 .
\[
f(x)=
\]
Finding a,b, and c in the Standard Form
Write the quadratic function in standard form.
\[
f(x)=7 x^{2}-x+1
\]
\[
f(x)=
\]
Finding the Discriminant
Discriminant of a quadratic equation
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
\[
-2 x^{2}+3 x+8=0
\]
Discriminant:
Number of real solutions:
Finding the Quadratic Constant of Variation
Name:
5. The function $Q=0.003 t^{2}-0.625 t+25$ represents the amount of energy, in Joules, in a battery after t minutes of use.
a) State the amount of energy held by the battery immediately before it was used. [1]
\[
\begin{aligned}
Q & =0.003 t^{2}-0.625 t+25 \\
& =0.003(0)^{2}-0.625(0)+25 \\
Q & =25
\end{aligned}
\]
b) Calculate the number of minutes it takes for the energy to reach zero. [4]
Finding the Zeros by Completing the Square
Find the zeros of the quadratic equation \(2x^2 - 8x - 10 = 0\) by completing the square.