Quadratic Function

The standard form of the quadratic function is f (x) = ax 2 +bx+c where a ≠ 0. The graph of the quadratic function is in the form of a parabola. The quadratic formula is used to solve a quadratic equation ax 2 + bx + c = 0 and is given by x

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Finding a quadratic function with a parabola

Using the Quadratic Formula Just put the values of a, b and c into the Quadratic Formula, and do the calculations. Example: Solve 5x 2 + 6x + 1 = 0 Coefficients are: a = 5, b = 6, c = 1 Quadratic

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Now, we can write our function for the quadratic as follows (since if we solve the following for 0, we'll get our 2 intersection points): f ( x) = ( x + 2) ( x − 1) We can expand this to give: f(x) = x 2 + x − 2 This is a quadratic function

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How to Write a Quadratic Function in Standard Form

Substitute the value of a into the equation from Step 1. In this example, substituting a into y = a (x - 2)^2 + 3 y = a(x −2)2 + 3 results in y = 5 (x - 2)^2 + 3 y = 5(x− 2)2 + 3 Square the expression inside the parentheses

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Quadratic Functions

Step 1: Write the general formula for a quadratic function y = ax^2 + bx + c. Step 2: Substitute each given point in the above function to get three equations: (1, 4): 4 = a (1^2) + b