Quadratics & Polynomials - SAT Math
Card 0 of 100
Standard form of a quadratic equation
Standard form of a quadratic equation
$y = ax^2 + bx + c$.
$y = ax^2 + bx + c$.
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Factored form of a quadratic
Factored form of a quadratic
$y = a(x - r_1)(x - r_2)$, where $r_1$ and $r_2$ are the roots.
$y = a(x - r_1)(x - r_2)$, where $r_1$ and $r_2$ are the roots.
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Vertex form of a quadratic
Vertex form of a quadratic
$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
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Formula for the axis of symmetry of $y = ax^2 + bx + c$.
Formula for the axis of symmetry of $y = ax^2 + bx + c$.
$x = \frac{-b}{2a}$.
$x = \frac{-b}{2a}$.
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What is the quadratic formula?
What is the quadratic formula?
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
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What is the definition of the discriminant?
What is the definition of the discriminant?
$D = b^2 - 4ac$.
$D = b^2 - 4ac$.
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What does a positive discriminant mean?
What does a positive discriminant mean?
Two distinct real roots.
Two distinct real roots.
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What does a zero discriminant mean?
What does a zero discriminant mean?
One real root (repeated).
One real root (repeated).
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What does a negative discriminant mean?
What does a negative discriminant mean?
No real roots (two complex roots).
No real roots (two complex roots).
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Perfect square trinomial expansion: $(x + y)^2$
Perfect square trinomial expansion: $(x + y)^2$
$x^2 + 2xy + y^2$.
$x^2 + 2xy + y^2$.
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Perfect square trinomial expansion: $(x - y)^2$
Perfect square trinomial expansion: $(x - y)^2$
$x^2 - 2xy + y^2$.
$x^2 - 2xy + y^2$.
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What is the difference of squares identity?
What is the difference of squares identity?
$a^2 - b^2 = (a + b)(a - b)$.
$a^2 - b^2 = (a + b)(a - b)$.
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Sum and product of roots of $ax^2 + bx + c = 0$.
Sum and product of roots of $ax^2 + bx + c = 0$.
Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
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How does $a$ affect the direction of a parabola?
How does $a$ affect the direction of a parabola?
If $a > 0$, it opens upward; if $a < 0$, it opens downward.
If $a > 0$, it opens upward; if $a < 0$, it opens downward.
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How does the absolute value of $a$ affect a parabola?
How does the absolute value of $a$ affect a parabola?
Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
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Formula for the vertex $y$-coordinate using coefficients.
Formula for the vertex $y$-coordinate using coefficients.
$y = c - \frac{b^2}{4a}$.
$y = c - \frac{b^2}{4a}$.
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Zero-product property.
Zero-product property.
If $ab = 0$, then $a = 0$ or $b = 0$.
If $ab = 0$, then $a = 0$ or $b = 0$.
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Factoring rule for $x^2 - 9$.
Factoring rule for $x^2 - 9$.
$(x - 3)(x + 3)$.
$(x - 3)(x + 3)$.
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Factoring rule for $x^2 + 6x + 9$.
Factoring rule for $x^2 + 6x + 9$.
$(x + 3)^2$.
$(x + 3)^2$.
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Factoring rule for $x^2 - 6x + 9$.
Factoring rule for $x^2 - 6x + 9$.
$(x - 3)^2$.
$(x - 3)^2$.
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