SAT Math: Parabolas and Quadratic Functions 02

$\sqrt{x-a} =x-9$

If $a=3$ , what is the solution set of the equation above?

${9}$

${12}$

${7,12}$

${6,13}$

What are the solutions to $4x^2 +20x+24=0$ ?

$-\dfrac{5}{2} \pm \sqrt{2}$

$\dfrac{25}{4} \pm \sqrt{\dfrac{1}{4}}$

$\dfrac{25}{4} \pm \sqrt{\dfrac{5}{6}}$

$-\dfrac{5}{2} \pm \sqrt{\dfrac{1}{4}}$

$h=-4.9t^2 + 34t$

The equation above expresses the approximate height $h$ , in meters, of a ball $t$ seconds after it is launched vertical upwards from the ground with an initial velocity of 34 meters per second. After approximately how many seconds will the ball hit the ground?

$5$

$6$

$7$

$8$

In the xy-plane, the parabola with the equation $y=(x-15)^2$ intersects with the equation $y=49$ at two points, $A$ and $B$ . What is the length of $\overline{AB}$ ?

$-2$

$12$

$14$

$10$

In the xy-plane, the graph of function $f$ has x-intercepts at $4$ and $-5$ . Which of the following could define $f$ ?

$5x^2 -5x +2$

$x^2 +x -20$

$4x^2 +5x -20$

$x^2 -9x +20$

$y=a(x-3)(x+5)$

In the quadratic equation above, $a$ is a nonzero constant. The graph of the equation in the xy-plane is a parabola with the vertex $(c,d)$ . Which of the following is equal to $d$ ?

$-8a$

$-16a$

$-24a$

$-32a$