Quadratic Equations - SAT Math
Card 0 of 30
Factored form of a quadratic
Factored form of a quadratic
Tap to see back →
$y = a(x - r_1)(x - r_2)$, 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.
Find the axis of symmetry for $y = x^2 - 6x + 5$.
Find the axis of symmetry for $y = x^2 - 6x + 5$.
Tap to see back →
$x = 3$.
$x = 3$.
Find the vertex of $y = (x - 4)^2 + 1$.
Find the vertex of $y = (x - 4)^2 + 1$.
Tap to see back →
$(4, 1)$.
$(4, 1)$.
Find the vertex of $y = x^2 - 6x + 5$.
Find the vertex of $y = x^2 - 6x + 5$.
Tap to see back →
Vertex $(3, -4)$.
Vertex $(3, -4)$.
Formula for the axis of symmetry of $y = ax^2 + bx + c$.
Formula for the axis of symmetry of $y = ax^2 + bx + c$.
Tap to see back →
$x = \frac{-b}{2a}$.
$x = \frac{-b}{2a}$.
Formula for the vertex $y$-coordinate using coefficients.
Formula for the vertex $y$-coordinate using coefficients.
Tap to see back →
$y = c - \frac{b^2}{4a}$.
$y = c - \frac{b^2}{4a}$.
How does $a$ affect the direction of a parabola?
How does $a$ affect the direction of a parabola?
Tap to see back →
If $a > 0$, it opens upward; if $a < 0$, it opens downward.
If $a > 0$, it opens upward; if $a < 0$, it opens downward.
How does the rate of change of a quadratic function behave?
How does the rate of change of a quadratic function behave?
Tap to see back →
It changes linearly with $x$ (not constant).
It changes linearly with $x$ (not constant).
If $y = -x^2 + 4x + 5$, find the vertex.
If $y = -x^2 + 4x + 5$, find the vertex.
Tap to see back →
Vertex $(2, 9)$.
Vertex $(2, 9)$.
If $y = -x^2 + 4x + 5$, what is the axis of symmetry?
If $y = -x^2 + 4x + 5$, what is the axis of symmetry?
Tap to see back →
$x = 2$.
$x = 2$.
If $y = 2(x + 1)^2 - 8$, what is the vertex?
If $y = 2(x + 1)^2 - 8$, what is the vertex?
Tap to see back →
$(-1, -8)$.
$(-1, -8)$.
If minimum=3 and maximum=27, what is the range?
If minimum=3 and maximum=27, what is the range?
Tap to see back →
$24$.
$24$.
Solve $2x^2 = 50$.
Solve $2x^2 = 50$.
Tap to see back →
$x^2 = 25 \Rightarrow x = \pm5$.
$x^2 = 25 \Rightarrow x = \pm5$.
Solve $x^2 - 4x - 5 = 0$.
Solve $x^2 - 4x - 5 = 0$.
Tap to see back →
$(x - 5)(x + 1) = 0 \Rightarrow x = 5$ or $x = -1$.
$(x - 5)(x + 1) = 0 \Rightarrow x = 5$ or $x = -1$.
Solve $x^2 + 2x - 15 = 0$.
Solve $x^2 + 2x - 15 = 0$.
Tap to see back →
$(x + 5)(x - 3) = 0 \Rightarrow x = -5$ or $x = 3$.
$(x + 5)(x - 3) = 0 \Rightarrow x = -5$ or $x = 3$.
Solve $x^2 + 7x + 10 = 0$.
Solve $x^2 + 7x + 10 = 0$.
Tap to see back →
$(x + 5)(x + 2) = 0 \Rightarrow x = -5$ or $x = -2$.
$(x + 5)(x + 2) = 0 \Rightarrow x = -5$ or $x = -2$.
Solve $x^2 = 16$.
Solve $x^2 = 16$.
Tap to see back →
$x = \pm4$.
$x = \pm4$.
Solve using the quadratic formula: $x^2 + 3x - 10 = 0$.
Solve using the quadratic formula: $x^2 + 3x - 10 = 0$.
Tap to see back →
$x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-10)}}{2} = \frac{-3 \pm 7}{2} \Rightarrow x = 2$ or $x = -5$.
$x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-10)}}{2} = \frac{-3 \pm 7}{2} \Rightarrow x = 2$ or $x = -5$.
Standard form of a quadratic equation
Standard form of a quadratic equation
Tap to see back →
$y = ax^2 + bx + c$.
$y = ax^2 + bx + c$.
Vertex form of a quadratic
Vertex form of a quadratic
Tap to see back →
$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
Vertex of $y = |x + 4| - 5$
Vertex of $y = |x + 4| - 5$
Tap to see back →
$(-4, -5)$.
$(-4, -5)$.
What does a negative discriminant mean?
What does a negative discriminant mean?
Tap to see back →
No real roots (two complex roots).
No real roots (two complex roots).
What does a positive discriminant mean?
What does a positive discriminant mean?
Tap to see back →
Two distinct real roots.
Two distinct real roots.
What does a zero discriminant mean?
What does a zero discriminant mean?
Tap to see back →
One real root (repeated).
One real root (repeated).
What is the definition of the discriminant?
What is the definition of the discriminant?
Tap to see back →
$D = b^2 - 4ac$.
$D = b^2 - 4ac$.
What is the maximum value of $y = -2(x + 3)^2 + 5$?
What is the maximum value of $y = -2(x + 3)^2 + 5$?
Tap to see back →
5 (occurs at $x = -3$).
5 (occurs at $x = -3$).
What is the minimum value of $y = (x - 4)^2 + 1$?
What is the minimum value of $y = (x - 4)^2 + 1$?
Tap to see back →
1 (occurs at $x = 4$).
1 (occurs at $x = 4$).
What is the quadratic formula?
What is the quadratic formula?
Tap to see back →
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
What is the vertex of $y = -3(x + 1)^2 + 4$?
What is the vertex of $y = -3(x + 1)^2 + 4$?
Tap to see back →
$(-1, 4)$.
$(-1, 4)$.
What is the vertex of $y = (x - 2)^2 + 5$?
What is the vertex of $y = (x - 2)^2 + 5$?
Tap to see back →
$(2, 5)$.
$(2, 5)$.