Solving Nonlinear Functions - SAT Math
Card 1 of 7
State the quadratic formula used to solve $ax^2 + bx + c = 0$.
State the quadratic formula used to solve $ax^2 + bx + c = 0$.
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$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Derived by completing the square on the general quadratic form.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Derived by completing the square on the general quadratic form.
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Identify the vertex form of a quadratic function.
Identify the vertex form of a quadratic function.
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$y = a(x-h)^2 + k$. Shows vertex $(h,k)$ and stretch factor $a$ explicitly.
$y = a(x-h)^2 + k$. Shows vertex $(h,k)$ and stretch factor $a$ explicitly.
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What is the discriminant in the quadratic formula?
What is the discriminant in the quadratic formula?
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$b^2 - 4ac$. Expression under the square root that determines root types.
$b^2 - 4ac$. Expression under the square root that determines root types.
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Find the roots of $x^2 - 5x + 6 = 0$.
Find the roots of $x^2 - 5x + 6 = 0$.
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$x = 2$ or $x = 3$. Factor: $(x-2)(x-3) = 0$ gives roots.
$x = 2$ or $x = 3$. Factor: $(x-2)(x-3) = 0$ gives roots.
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What is the standard form of a quadratic equation?
What is the standard form of a quadratic equation?
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$ax^2 + bx + c = 0$. General form with degree 2 polynomial set to zero.
$ax^2 + bx + c = 0$. General form with degree 2 polynomial set to zero.
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What is the product of the roots of $ax^2 + bx + c = 0$?
What is the product of the roots of $ax^2 + bx + c = 0$?
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$\frac{c}{a}$. Vieta's formula for product of roots.
$\frac{c}{a}$. Vieta's formula for product of roots.
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What is the sum of the roots of $ax^2 + bx + c = 0$?
What is the sum of the roots of $ax^2 + bx + c = 0$?
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$-\frac{b}{a}$. Vieta's formula for sum of roots.
$-\frac{b}{a}$. Vieta's formula for sum of roots.
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