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"Quadratic Function" Explained

Function that looks like a “u” when graphed. Has 3 forms standard, factor and vertex form.

Key Idea: Quadratic Function

A quadratic function is a function that creates a U-shaped graph called a parabola.
It represents equations where the highest power of x is 2.

General Rule:

Quadratic functions can be written in three main forms:

  • Standard Form: y=ax^2+bx+c

  • Factored Form: y=a(x−r_1)(x−r_2)

  • Vertex Form: y=a(x−h)^2+k

The coefficient a determines whether the parabola opens upward (a > 0) or downward (a < 0).

Why this matters for the SAT:

Quadratic functions appear in algebra and graphing problems.
Knowing the different forms helps you quickly identify key features like the vertex, zeros (roots), and direction of opening—essential for solving and interpreting quadratic equations.

"Standard Quadratic Form" Explained

ax^2 + bx + c.
a,b and c are used in quadratic formula.
c is y-intercept.

Key Idea: Standard Quadratic Form

The standard form of a quadratic function is:

y=ax^2+bx+c

General Rule:

  • , , and are coefficients used in the quadratic formula:

x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}

  • c represents the y-intercept of the parabola.

  • aa determines the direction of the parabola (upward if a>0, downward if a<0).

Why this matters for the SAT:

Standard form is commonly used to solve quadratic equations and identify key features like y-intercept and coefficients for the quadratic formula.
It’s essential for graphing and algebra problems involving quadratics.

"Factor Quadratic Form" Explained

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"Vertex Quadratic Form" Explained

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