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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