ACT · Mathematics

Quadratic equations

21 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 21 questions

What is the greater solution of $x^{2} - 5 x - 14 = 0$ ?
What is the greater solution of $x^{2} + 2 x - 15 = 0$ ?
What is the greater solution of $x^{2} + x = 0$ ?
What is the greater solution of $x^{2} - 7 x + 6 = 0$ ?
What is the greater solution of $x^{2} + 12 x + 35 = 0$ ?
What is the greater solution of $x^{2} - 1 = 0$ ?
What is the greater solution of $x^{2} + 9 x + 18 = 0$ ?
What is the greater solution of $x^{2} - 8 x + 12 = 0$ ?
What is the greater solution of $x^{2} - 2 x - 35 = 0$ ?
What is the greater solution of $x^{2} - 8 x + 7 = 0$ ?
What is the greater solution of $x^{2} - 6 x + 8 = 0$ ?
What is the greater solution of $x^{2} + 5 x - 14 = 0$ ?
What is the greater solution of $x^{2} + 9 x + 20 = 0$ ?
What is the greater solution of $x^{2} - 10 x + 16 = 0$ ?
What is the greater solution of $x^{2} - 2 x - 8 = 0$ ?
For which value of $c$ does the line $y = 5 x + c$ touch the parabola $y = x^{2} - 3 x + 7$ at exactly one point?
A ball's height in feet is $h (t) = - 16 t^{2} + 64 t + 80$ , where $t$ is time in seconds after launch. At what time $t > 0$ does the ball hit the ground?
The equation $x^{2} - 6 x + k = 0$ has two real solutions that differ by $4$ . What is the value of $k$ ?
A parabola $y = a x^{2} + b x + c$ passes through $(0, 3)$ and has its vertex at $(2, - 1)$ . What is the value of $ab c$ ?
The height of a ball in feet is $h (t) = - 16 t^{2} + 48 t + 64$ , where $t$ is time in seconds. What is the maximum height?
What is the sum of the squares of all real solutions of $x^{4} - 5 x^{2} + 4 = 0$ ?

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