Exam 8: Quadratic Equations and Functions

Fill in the blank with one of the words or phrases listed below. -The graph of $f ( x ) = ( x - h ) ^ { 2 } + k$ has vertexــــــــــــــــــ

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = x ^ { 2 } - 5 x + 1$

Solve. - $2 x ^ { 2 / 3 } - 4 x ^ { 1 / 3 } - 30 = 0$

Use the quadratic formula to solve the equation. - $6 x ^ { 2 } + 24 x = - 19$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = 5 x ^ { 2 } - 1$

Use the square root property to solve the equation. $x ^ { 2 } + 81 = 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = ( x - 1 ) ^ { 2 } - 1$

Fill in the blank with one of the words or phrases listed below. -The helps us find the number and type of solutions of a quadratic equation.

Use the square root property to solve the equation. $x ^ { 2 } = 22$

Use the square root property to solve the equation. $( x + 1 ) ^ { 2 } = - 63$

Solve. -Use the formula $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$ . Find the rate, $\mathrm { r }$ , at which $\$ 1400$ grows to $\$ 1573$ in 2 years.

Solve. -A projectile is fired from a cliff 400 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with an initial velocity of 290 feet per second. The height $h$ of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 290 ) ^ { 2 } } + x + 400$ , where $x$ is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the projectile.

Use the quadratic formula to solve the equation. - $3 x ^ { 2 } + 12 x + 1 = 0$

Solve the equation. - $2 x ^ { 2 } - 7 x = 9$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 4 x \geq - 3$

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 4 x + 40 = 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - ( x + 1 ) ^ { 2 } + 4$

Solve. - $x - \sqrt { 3 x } = 2$

Solve the equation. - $( 3 x - 1 ) ^ { 2 } - 10 ( 3 x - 1 ) = - 21$

Solve. -A rocket is launched from the top of a cliff. The height, $\mathrm { s } ( \mathrm { t } )$ , of the rocket after $\mathrm { t }$ seconds is given by the equation $s ( t ) = - 16 t ^ { 2 } + 120 t + 48$ . How long after the rocket is launched will it strike the ground? Round to the nearest tenth of a second, if necessary.