Exam 3: Quadratic Functions and Equations; Inequalities

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - $7 x ^ { 2 } = 21 x$

Solve by completing the square to obtain exact solutions. - $25 x ^ { 2 } + 50 x + 16 = 0$

Solve graphically. Round solutions to three decimal places, where appropriate. - $3 x ^ { 2 } - 5 = 6 x$

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = - x ^ { 2 } + 5 x - 3$

Solve the problem. -Your company uses the quadratic model $y = - 11 x ^ { 2 } + 350 x$ to represent how many units ( $y$ ) of a new product will be sold $( x )$ weeks after its release. How many units can you expect to sell in week 12?

Solve. - $\sqrt [ 3 ] { 4 x + 7 } = - 3$

Solve. - $\frac { 8 } { y + 5 } - \frac { 2 } { y - 5 } = \frac { 10 } { y ^ { 2 } - 25 }$

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 2 x - \frac { 15 } { 2 }$

Use the given graph to find the x-intercepts and zeros of the function. -

Find the axis of symmetry of the given function. - $f ( x ) = x ^ { 2 } - 17 x + 10$

Graph. -

Match the equation to the correct graph. - $y = x ^ { 2 } - 7$

Use the quadratic formula to find the exact solutions. - $x ^ { 2 } = 15 + 3 x$

Find the vertex of the parabola. - $g ( x ) = x ^ { 2 } - 13 x + 6$

Match the equation to the correct graph. - $y = - ( x + 3 ) ^ { 2 } + 2$

Graph. - $f(x)=4 x^{2}-3 x-8$

Solve the inequality and graph the solution set. - $| x | > 5$

Solve. - $12 x ^ { 3 } - 30 x ^ { 2 } + 10 x - 25 = 0$

Find the vertex of the parabola. - $f ( x ) = 2 x ^ { 2 } - 12 x + 16$

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - $25 x ^ { 2 } - 10 x + 1 = 0$