Solve $x^2-16=0$

Solve $2x^2-5x=12$

Solve $16a^2-25=0$

Solve for $x$: $\;x^2=5$

Solve for $y$: $\; (y+4)^2=25$

Table 1 in the introduction to this section gives the vertical rise of the Comstock Express chair lift as $1\text{,}253$ feet and the length of the chair lift as $5\text{,}649$ feet. To the nearest foot, find the horizontal distance covered by a person riding this lift.

Mini Lecture
Solve.

1. $y^2=8$

2. $3a^2=54$

3. $(a-5)^2=75$

4. $(4a-5)^2=36$

5. $(3a+6)^2=45$

6. $\left(x+\displaystyle\frac{1}{2}\right)^2=\displaystyle\frac{7}{4}$

Write the correct final term to make $x^2-14x$ a perfect square trinomial.

Write the correct final term to make $x^2+20x$ a perfect square trinomial.

Write the correct final term to make $x^2+5x$ a perfect square trinomial.

Solve $x^2-4x+3=0$ by completing the square.

Solve $3x^2+24x-27=0$ by completing the square.

Solve $y^2-4y=0$

Solve by completing the square: $x^2+5x-2=0$

Mini Lecture
Add a last term to complete the square.

1. $x^2+16x$

2. $y^2-8y$

3. $x^2+7x$

Solve by completing the square.

4. $x^2-6x=16$

Simplify the quadratic formula if $a=4$, $b=-4$, and $c=-15$.

Simplify the quadratic formula if $a=3$, $b=6$, and $c=1$.

Solve $x^2-4x-5=0$ by using the quadratic formula.

Solve $x^2-9=0$

Solve for $x$: $\; x^2+2x=\displaystyle\frac{3}{2}$

Solve for $x$: $\; (x+2)(x-1)=9$

Mini Lecture
Solve using the quadratic formula.

1. $x^2+5x+6=0$

2. $x^2-5x=7$

3. $3x^2=-4x+2$

Enrichment
Deriving the quadratic formula.

Add: $(3+4i)+(2-6i)$

Subtract: $(5-4i)-(6-i)$

Simplify: $(2-5i)-(3+7i)+(2-i)$

Multiply: $4i(3+5i)$

Multiply: $(3+2i)(4-3i)$

Divide $\dfrac{2+i}{5+2i}$

Mini Lecture
Combine.

1. $(6+2i)-10i$

2. $9-i+(2-i)$

Multiply.

3. $2i(8-7i)$

4. $(3+5i)(3-5i)$

Divide.

5. $\dfrac{2+i}{2-i}$

Write as a complex number:

1. $\sqrt{-4}$

2. $\sqrt{-36}$

3. $\sqrt{-7}$

4. $\sqrt{-75}$

Solve $(x+2)^2=-9$

Solve $\dfrac{1}{10}x^2-\dfrac{1}{5}x=-\dfrac{1}{2}$

Solve: $(2x-3)(2x-1)=-4$

Mini Lecture
Simplify.

1. $\sqrt{-49}$

2. $\sqrt{-8}$

Solve.

3. $2x^2+5x=12$

4. $\left(x+\dfrac{1}{2}\right)^2=-\dfrac{9}{4}$

5. $\dfrac{1}{2}x^2+\dfrac{1}{3}x+\dfrac{1}{6}=0$

Graph $y=(x-2)^2$

Graph $y=(x+1)^2-3$

Find the intercepts for $y=x^2-6x+5$.

Find the intercepts for $y=(x+1)^2-3$.

Find the intercepts for $y=x^2+2x-5$ and use them to sketch the graph of the equation.

Mini Lecture
Graph.

1. $y=x^2-4$

2. $y=(x+2)^2$

3. $y=(x+2)^2-3$