Writing Unique Quadratic Equations

Write an equation for a quadratic function that has a vertex of (3, 5) and passes through the point (5, - 3).

• $y=-2\left(x-3\right)^2+5$

• $y=-4\left(x-3\right)^2+5$

• $y=-\frac{1}{2}\left(x-5\right)^2-3$

• $y=-\frac{1}{8}\left(x+3\right)^2+5$

Write an equation for a quadratic function that has a vertex of ( -2, - 9) and an x-intercept of (1, 0).

• $y=-\left(x+2\right)^2-9$

• $y=\left(x+2\right)^2-9$

• $y=\frac{5}{2}\left(x+2\right)^2-9$

• $y=9\left(x-2\right)^2-9$

Write an equation for a quadratic function that has x-intercepts at ( -7, 0) and (5, 0) and passes through the point ( - 4, - 9).

• $y=\frac{1}{3}\left(x-5\right)\left(x+7\right)$

• $y=-\frac{1}{3}\left(x-5\right)\left(x+7\right)$

• $y=\frac{1}{3}\left(x+5\right)\left(x-7\right)$

• $y=-\frac{1}{3}\left(x+5\right)\left(x-7\right)$

Write an equation for a quadratic function that has a y-intercept of (0, 11) and a vertex of ( -4, 3).

• $y=-\frac{1}{2}\left(x\right)^2+11$

• $y=\frac{1}{2}\left(x\right)^2+11$

• $y=-\frac{1}{2}\left(x+4\right)^2+3$

• $y=\frac{1}{2}\left(x+4\right)^2+3$

Write a quadratic equation for a parabola that has a vertex at (2, 0) and passes through the point (0, - 12).

• $y=3\left(x+2\right)^2$

• $y=-3\left(x+2\right)^2$

• $y=3\left(x-2\right)^2$

• $y=-3\left(x-2\right)^2$

Write an equation for a quadratic function that has x-intercepts at ( -3, 0) and (10, 0) and passes through the point ( 1, - 9).

• $y=-\frac{1}{4}\left(x+3\right)\left(x-10\right)$

• $y=\frac{1}{4}\left(x+3\right)\left(x-10\right)$

• $y=\frac{1}{114}\left(x+3\right)\left(x-10\right)$

• $y=\frac{9}{22}\left(x-3\right)\left(x+10\right)$

Write a unique quadratic equation that passes through the points (-3, -10), (0, -7), (2, 5) and (4, 25).