Properties of Quadratics

This worksheet covers Properties of Quadratics, which is part of the Quadratics module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.

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Properties of Quadratics

Quadratics • SAT Math

Set 4 — Mastery

What is the vertex of the quadratic function given by the equation $f(x) = 2x^{2} - 8x + 5$ ?

(2, -3)

(4, -3)

(2, 5)

(0, 5)

Which of the following is the factored form of the quadratic equation $x^{2} - 5x + 6$ ?

$(x - 2)(x - 3)$

$(x + 2)(x + 3)$

$(x - 1)(x - 6)$

$(x - 3)(x - 2)$

For the quadratic $f(x) = -x^{2} + 4x - 3$ , what is the maximum value of the function?

What are the roots of the quadratic equation $3x^{2} - 12x + 9 = 0$ ?

2, 2

1, 3

0, 3

If the quadratic $y = ax^{2} + bx + c$ opens downward, which of the following must be true?

$a < 0$

$a > 0$

$b > 0$

$c > 0$

What is the axis of symmetry for the quadratic $f(x) = 4x^{2} - 16x + 15$ ?

For which value of $k$ does the quadratic $x^{2} - kx + 12$ have roots that are both integers?

What is the discriminant of the quadratic equation $2x^{2} - 4x + 2 = 0$ ?

-8

If the quadratic $f(x) = x^{2} + px + q$ has roots that are equal, what is the relationship between $p$ and $q$ ?

$p^{2} = 4q$

$p + q = 0$

$p = 2q$

$p + q = 1$

10.

For the quadratic $f(x) = 5x^{2} + 10x + 5$ , what is the value of $f(-2)$ ?

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