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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 5 — Mastery

What is the vertex of the parabola given by the equation $y = 2x^{2} - 8x + 3$ ?

( $2, -5)$

( $-2, 5)$

( $4, -13)$

( $-4, 13)$

Which of the following equations represents a parabola that opens downwards?

$y = -3x^{2} + 4x - 2$

$y = 5x^{2} + 2x + 1$

$y = 0.5x^{2} - 3x$

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

The quadratic function $f(x) = x^{2} + bx + c$ has a minimum value of $-4$ at $x = 2$ . What is the value of $b$ ?

$-4$

$0$

$4$

$8$

If the roots of the quadratic equation $x^{2} - kx + 12 = 0$ are both integers, what is the maximum value of $k$ ?

$10$

$11$

$12$

$14$

What is the axis of symmetry for the quadratic function $f(x) = -x^{2} + 6x - 5$ ?

$3$

$-3$

$6$

$5$

For the quadratic $y = x^{2} + 4x + 4$ , what are the coordinates of the vertex?

( $-2, 0)$

( $-2, -4)$

( $0, 4)$

( $2, 4)$

If $x^{2} + mx + n = 0$ has roots $-3$ and $-4$ , what is the value of $m$ ?

$7$

$11$

$12$

$14$

A quadratic function has zeros at $x = 1$ and $x = 7$ . What is the vertex of this parabola?

( $4, -9)$

( $4, -1)$

( $4, 0)$

( $2, 6)$

For the quadratic function $f(x) = 3x^{2} - 18x + 24$ , what is the minimum value of $f(x)$ ?

$-3$

$0$

$3$

$6$

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