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Working with Percentages and Proportions
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Negative Rational Exponents
Roots and Radicals
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Product and Quotient of Functions
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Laws of Exponents
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Vertical Line Test
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Multiplying Polynomials
Solving Quadratic and Polynomial Equations
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Quadratic Functions: Parabolas

Quadratic Functions

A Quadratic (or Second-Degree) Function is a function of the form f(x) = ax2 + bx + c, where a, b and c are real numbers and a 0. This form is called the General Form of a Quadratic Function.

The graph of a quadratic function is a parabola with a "turning point" called the vertex.

The domain of a quadratic function is all real numbers.

f(x) = x2 is concave up while f(x) = -x2 + 4x + 21 concave down.

So, when looking at the general form for a quadratic function, f(x) = ax2 + bx + c, what does a tell us about the graph?

The sign of a tells us whether the parabola is concave up or concave down.

There is another form of a quadratic function, called the Standard Form of a Quadratic Function

y = a(x - h)2 + k is a quadratic function with vertex (h, k) and axis of symmetry x = h. It opens up if a > 0 and down if a < 0. It is wider than f(x) = x2 if -1 < a < 1, and narrower if a > 1 or if a < -1.


Now if the function is in General Form, f(x) = ax2 + bx + c, the vertex is not as obvious. There is a helpful formula, however:

Given a quadratic function f(x) = ax2 + bx + c, the vertex is the point:

When you graph a Quadratic Function (parabola), you should show:

  • Vertex
  • Axis of Symmetry
  • x-intercepts (or ) if it has any zeros
  • y-intercept


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