# Can You Solve This Algebra Problem?

Last Updated on September 30, 2020 by A Plus In-Home Tutors

**Quadratic Functions**

A quadratic function is defined by `f(x) = ax^2 + bx + c`. To make it easier, just replace the `f(x)` with `y` and treat as you have done in the past.

With a function in standard form `ax^2 + bx + c`, the vertex is `-b/(2a)` and the **axis of symmetry** is `x = -b/(2a)`. The **vertex** is the point on the PARABOLA where the **slope changes sign** from positive to negative or vice-versa. The axis of symmetry, you recall, is the line when the parabola can be “flipped” or “folded over” and still be symmetrical in shape.

**You should plot at least 5 points** when making a graph of the equation and **DO NOT use a ruler** to connect the points, this is a parabola, NOT a linear equation.

Where the **parabola crosses the x-axis are called the ROOTS** of the equation. **These are also the x-intercepts!**

**ROOTS, ZEROES, X-INTERCEPTS and ANSWERS ALL MEAN THE SAME THING!**

You can find the ROOTS easily by setting y = 0 and solving the quadratic equation with the factoring techniques from Chapter 6 and 10

OR

making a graph and seeing the 2 points (up to actually) where the parabola crosses the x-axis.

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