Exam 14: Quadratic Equations

Determine if the roots of $36 x^{2}+48 x+61=0$ are real or nonreal, and whether they are equal or unequal.

Plot $y=-5 x^{2}+4 x+1$ and label the vertex.

Solve for $x$ and $y: 2 y-x=5$ $x^{2}+y^{2}=25$

Solve this radical equation for $x$ and check: $\sqrt{2 x^{2}-1}+15=22$

When a certain number is divided by five and added to its reciprocal, the result is 1.2. What is the number?

Solve for $x$ by completing the square: $2 x^{2}+5 x+2=0$

Solve for $x$ by factoring: $(x+3)^{2}=6 x+25$

Plot $y=5 x^{2}+18 x-8$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

Write a quadratic equation that has roots $x=4$ and $x=-2$ .

A driver calculates that if she decreases her average speed by $15 \mathrm{mi} . / \mathrm{h}$ , she would travel her 650 -mile trip in $3.0 \mathrm{hr}$ more time than at her usual speed. What is her usual speed?

Solve for $x$ by completing the square: $x^{2}+8 x+1=0$

Use the quadratic formula to solve for $x$ to three significant digits: $3 x^{2}+33 x+4=0$

After the largest possible circle is cut from a square, the area of the paper remaining is $3.5 \mathrm{~cm}^{2}$ . Determine the radius of the circle.

Solve and check this equation. Assume $p$ is nonzero: $3 p^{2}-2 p=7.42 p$

Determine if the roots of $-18 x^{2}+65 x+61=0$ are real or nonreal, and whether they are equal or unequal.

Solve for $x$ by factoring: $\frac{2 x+1}{5}=\frac{4}{x-1}$

Solve for all real values of $x: x^{2 / 3}-x^{1 / 3}=6$

Plot $y=-x^{2}+2 x+3$ and label the vertex.

Solve for $x$ by completing the square: $9 x^{2}+12 x-22=0$

A square had one side increased by $2.00 \mathrm{~m}$ , and the other decreased by $1.00 \mathrm{~m}$ . The area of the rectangle that resulted was half the area of the original square. What size was the square?