Exam 2: Linear and Quadratic Functions

Solve the problem. -A projectile is fired from a cliff 300 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 270 feet per second. The height h of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 270 ) ^ { 2 } } + x + 300$ , Where x is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the Projectile.

Solve the inequality. Express your answer using interval notation. Graph the solution set. - $| x | > - 4$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = - x ^ { 2 } - 10 x$

Solve the problem. -Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) = g(x).

Match the graph to one of the listed functions. -

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=13 g(x)=-3x

Solve the problem. -A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $176 \mathrm { ft } / \mathrm { sec }$ , and the gorge is $448 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( \mathrm { h } = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { \mathrm { O } } \mathrm { t } + \right.$ $\mathrm { h } _ { \mathrm { O } }$ .)

Find the zero of the linear function. -g(x) = -x + 8

Determine the slope and y-intercept of the function. -h(x) = -2x - 6

Determine where the function is increasing and where it is decreasing. - $f ( x ) = - 4 x ^ { 2 } - 2 x - 11$

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=-2 x^{2}-20 x-53$ A) vertex (-5,-3) intercept (0,-53) B) vertex (-5,-3) intercept 0,- C) vertex $( 5 , - 3 )$ intercept $\left( 0 , - \frac { 31 } { 2 } \right)$ D) vertex $( 5 , - 3 )$ intercept $( 0 , - 53 )$

Solve the equation. - $|3 m + 6| = 9$

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $P ( x ) = ( 4 x - 6 ) ^ { 2 } - 6 ( 4 x - 6 ) + 5$

Solve the inequality. Express your answer using interval notation. Graph the solution set. - $| x | < - 3$

Use a graphing calculator to plot the data and find the quadratic function of best fit. -The number of housing starts in one beachside community remained fairly level until 1992 and then began to increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator to Plot a scatter diagram. What is the quadratic function of best fit? Year, Housing Starts, H 1 200 2 210 3 230 4 240 5 250 6 230 7 215 8 208

Plot a scatter diagram. - x 24 -13 7 -10 -6 17 6 18 10 1 y 56 26 41 -12 -2 29 7 71 -9 5 A) B) C) D)

Determine the domain and the range of the function. - $f ( x ) = - x ^ { 2 } + 4 x + 5$

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. -Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program Versus their current GPAs. Entering GPA Current GPA 3.5 3.6 3.8 3.7 3.6 3.9 3.6 3.6 3.5 3.9 3.9 3.8 4.0 3.7 3.9 3.9 3.5 3.8 3.7 4.0

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } + 3 x + 6$