Chapter 9

Solve quadratic equation by completing the square. \(\frac{x^{2}}{6}-\frac{x}{3}-1=0\)

Express each function as a set of ordered pairs. \(g(x)=x-|x| ;\) domain: the set of integers from \(-2\) to 2 inclusive

Graph the parabola whose equation is given $$y=-3 x^{2}+6 x-2$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$9-6 x+x^{2}=0$$

Solve each quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. Simplify radicals, if possible. $$x^{2}-10 x+25=3$$

Solve quadratic equation by completing the square. \(\frac{x^{2}}{6}+x-\frac{3}{2}=0\)

Solve each quadratic equation using the quadratic formula. $$5 y^{2}=6 y-7$$

Find and simplify. \(\frac{f(x)-f(h)}{x-h}\) $$f(x)=6 x+7$$

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=(x-3)^{2}+2$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$4 x^{2}-16=0$$

Solve quadratic equation by completing the square. \((x+2)(x-3)=1\)

Solve each quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. Simplify radicals, if possible. $$x^{2}+2 x+1=5$$

Find and simplify. \(\frac{f(x)-f(h)}{x-h}\) $$f(x)=8 x+9$$

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=(x-4)^{2}+3$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$3 x^{2}-27=0$$

Solve quadratic equation by completing the square. \((x-5)(x-3)=1\)

Solve each quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. Simplify radicals, if possible. $$x^{2}+2 x+1=7$$

Solve each quadratic equation using the quadratic formula. $$8 x^{2}-9=5 x^{2}-30$$

Find and simplify. \(\frac{f(x)-f(h)}{x-h}\) $$f(x)=x^{2}-1$$

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=(x+5)^{2}-4$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$x^{2}+9 x=0$$

Solve quadratic equation by completing the square. \(x^{2}+4 b x=5 b^{2}\)

Solve each quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. Simplify radicals, if possible. $$y^{2}-14 y+49=12$$

Find and simplify. \(\frac{f(x)-f(h)}{x-h}\) $$f(x)=x^{3}-1$$

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=(x+6)^{2}-5$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$x^{2}-6 x=0$$

Solve quadratic equation by completing the square. \(x^{2}+6 b x=7 b^{2}\)

Solve each quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. Simplify radicals, if possible. $$y^{2}-14 y+49=18$$

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=2(x-1)^{2}-3$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$\frac{3}{4} x^{2}-\frac{5}{2} x-2=0$$

Explain how to complete the square for a binomial. Use \(x^{2}+6 x\) to illustrate your explanation.

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=2(x-1)^{2}-4$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$\frac{1}{3} x^{2}-\frac{1}{2} x-\frac{3}{2}=0$$

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

The function \(f(x)=0.76 x+171.4\) models the cholesterol level of an American man as a function of his age, \(x,\) in years. Find and interpret \(f(20)\)

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=-3(x+2)^{2}+5$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib \((3 x-2)^{2}=10\)

Determine whether statement "makes sense" or "does not make sense" and explain your reasoning. When I complete the square, I convert a quadratic equation into an equivalent equation that can be solved by the square root property.

The personnel manager of a roller skate company knows that the company's weekly revenue, \(R,\) in thousands of dollars, can be modeled by the formula $$R=-2 x^{2}+36 x$$ where \(x\) is the price of a pair of skates, in dollars. A job applicant promises the personnel manager an advertising campaign guaranteed to generate 200,000 dollar in weekly revenue. Substitute 200 for \(R\) in the given formula and solve the equation. Are the solutions real numbers? Explain why the applicant will or will not be hired in the advertising department.

The function \(f(x)=0.76 x+171.4\) models the cholesterol level of an American man as a function of his age, \(x,\) in years. Find and interpret \(f(50)\)

Find the vertex for the parabola whose equation is given by first writing the equation in the form \(y=a x^{2}+b x+c\) $$y=-3(x+4)^{2}+6$$

Solve each equation by the method of your choice. Simplify irrational solutions, if possib $$(4 x-1)^{2}=15$$

A football is kicked straight up from a height of 4 feet with an initial speed of 60 feet per second. The formula $$h=-16 t^{2}+60 t+4$$ describes the ball's height above the ground, \(h\), in feet, \(t\) seconds after it is kicked. Will the ball reach a height of 80 feet? Substitute 80 for \(h\) in the given formula and solve the equation. Are the solutions real numbers? Explain why the ball will or will not reach 80 feet.

Solve each equation by the method of your choice. Simplify irrational solutions, if possible $$\frac{x^{2}}{x+7}-\frac{3}{x+7}=0$$

Determine whether statement "makes sense" or "does not make sense" and explain your reasoning. When I complete the square for the binomial \(x^{2}+b x,\) I obtain a different polynomial, but when I solve a quadratic equation by completing the square, I obtain an equation with the same solution set.

What is the imaginary unit \(i ?\)

When the shot is released at an angle of \(65^{\circ},\) its height, \(y,\) in feet, can be modeled by $$y=-0.04 x^{2}+2.1 x+6.1$$ where \(x\) is the shot's horizontal distance, in feet, from its point of release. Use this model to solve parts (a) through (c) and verify your answers using the red graph. a. What is the maximum height, to the nearest tenth of a foot, of the shot and how far from its point of release does this occur? b. What is the shot's maximum horizontal distance, to the nearest tenth of a foot, or the distance of the throw? c. From what height was the shot released?

Solve each equation by the method of your choice. Simplify irrational solutions, if possible $$\frac{x^{2}}{x+9}-\frac{11}{x+9}=0$$

Explain how to write \(\sqrt{-64}\) as a multiple of \(i\)

If a relation is represented by a set of ordered pairs, explain how to determine whether the relation is a function.