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Solving Quadratic Equations

This worksheet covers Solving Quadratic Equations, which is part of the Introduction and Prerequisite module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Solving Quadratic Equations

Introduction and Prerequisite • SAT Math Destroyer Crash Course

Set 1 — Mastery

If the equation $x^{2} - 5x + 6 = 0$ is factored, what are the roots of the equation?

$2, 3$

$1, 6$

$-2, -3$

$3, -2$

A projectile is launched and its height $h$ in meters after $t$ seconds is given by the equation $h(t) = -4.9t^{2} + 20t + 1$ . What is the maximum height reached?

$21$

$25$

$30$

$20$

Which of the following equations has a discriminant of zero?

$x^{2} + 4x + 4 = 0$

$x^{2} + 5x + 6 = 0$

$x^{2} - 3x + 2 = 0$

$x^{2} + 3x + 2 = 0$

A rectangular garden is designed such that its length is twice its width. If the area of the garden is $72$ square meters, what are the dimensions of the garden?

Width: $6$ , Length: $12$

Width: $8$ , Length: $16$

Width: $9$ , Length: $18$

Width: $4$ , Length: $8$

What are the solutions to the equation $3x^{2} + 12x + 12 = 0$ ?

$-2$

$-3$

$-4$

$-6$

If $x^{2} - kx + 15 = 0$ has roots $3$ and $5$ , what is the value of $k$ ?

$8$

$5$

$15$

$10$

What is the vertex of the parabola represented by $y = x^{2} - 4x + 3$ ?

Vertex: $(2, -1)$

Vertex: $(4, 3)$

Vertex: $(1, 0)$

Vertex: $(3, 0)$

A quadratic function $f(x) = ax^{2} + bx + c$ has a maximum value of $10$ when $x = 2$ . What is the value of $a + b + c$ if $a < 0$ ?

$5$

$10$

$15$

$20$

Which of the following represents the quadratic equation of a parabola that opens downwards and has roots $-1$ and $3$ ?

$-1(x + 1)(x - 3)$

$1(x + 1)(x - 3)$

$-1(x - 1)(x + 3)$

$1(x - 1)(x + 3)$

10.

If the solutions to the quadratic equation $x^{2} - 4x + p = 0$ are both equal, what is the value of $p$ ?

$4$

$0$

$-4$

$8$

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