SAT Math Passport to Advanced Math Question Types Cheat Sheet

Key Facts

• A quadratic in standard form is $ax^2 + bx + c$, where $a \ne 0$.
• The factored form $a(x - r_1)(x - r_2)$ shows the zeros $x = r_1$ and $x = r_2$.
• The vertex form $a(x - h)^2 + k$ shows the vertex $(h, k)$ and the axis of symmetry $x = h$.
• The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for $ax^2 + bx + c = 0$.
• An exponential function has the form $f(x) = a(b)^x$, where $a$ is the initial value and $b$ is the growth or decay factor.
• Function notation means $f(a)$ is the output of the function $f$ when the input is $a$.
• Equivalent expressions have the same value for every allowed input, such as $(x + 3)^2 = x^2 + 6x + 9$.
• A rational equation can create extraneous solutions, so any solution must be checked in the original equation.

Vocabulary

Quadratic

A polynomial expression or equation with highest power $2$, usually written as $ax^2 + bx + c$.

Vertex

The highest or lowest point of a parabola, written as $(h, k)$ in the form $a(x - h)^2 + k$.

Discriminant

The expression $b^2 - 4ac$ that tells how many real solutions a quadratic equation has.

Exponential Function

A function in which the variable is in the exponent, such as $f(x) = a(b)^x$.

Function Notation

A way to name outputs of a function, where $f(x)$ means the value of function $f$ at input $x$.

Extraneous Solution

A value that appears during solving but does not satisfy the original equation.