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