91Ó°ÊÓ

Find an equation of the line that passes through \((2,-3)\) and is perpendicular to the line whose equation is \(y=\frac{x}{5}+6 .\) Write the equation in slope-intercept form.

The vertex of a quadratic function \(f(x)=a x^{2}+b x+c\) is given by the formula \(\left(-\frac{b}{2 a}, f\left(-\frac{b}{2 a}\right)\right) .\) Explain what is meant by the notation \(f\left(-\frac{b}{2 a}\right)\)

Dimensions of a Triangle. The height of a triangle is 4 meters longer than twice its base. Find the base and height if the area of the triangle is 10 square meters. Round to the nearest hundredth of a meter.

Explain why the quadratic formula, in most cases, is easier to use to solve a quadratic equation than is the method of completing the square.

Find the real-number solutions of \(x^{4}-3 x^{2}-2=0\) Rationalize the denominators of the solutions.

A table of values for \(f(x)=2 x^{2}-4 x+3\) is shown Explain why it appears that the vertex of the graph of \(f\) is the point \((1,1)\) (IMAGE CANNOT COPY)

Look Alikes . . . a. \(x^{2}-4 x+20=0\) b. \(x^{2}-4 x-20=0\)

Solve: \(x^{6}+17 x^{3}+16=0\)

Look Alikes . . . a. \(a^{2}=6 a-3\) b. \(n^{2}=6 n+3\)

On an exam, a student was asked to solve the equation \(-4 w^{2}-6 w-1=0 .\) Her first step was to multiply both sides of the equation by \(-1 .\) She then used the quadratic formula to solve \(4 w^{2}+6 w+1=0\) instead. Is this a valid approach? Explain.