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Graph Quadratic Functions: Maxima and Minima




 
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Videos, worksheets, solutions, and activities to help Algebra students learn about how to graph quadratic functions (maxima and minima).

How to graph quadratic functions in general form?
The graph of a quadratic function
f(x) = ax2 + bx + c, a ≠ 0 is called a parabola.
1. It is always a cup-shaped curve.
2. It opens upward if a > 0 and opens downward if a < 0.
3. The vertical line \(x = \frac{{ - b}}{{2a}}\) is the line of symmetry.
4. It has a turning point, or vertex, at a point
\[\left( { - \frac{b}{{2a}},f\left( { - \frac{b}{{2a}}} \right)} \right)\]
5. The vertex is a maxima if a < 0 and a minima if a > 0.

Graphing Quadratic Functions in General Form
Students learn to graph quadratic functions that are written in f(x) = ax2 + bx + c form, using the vertex, the y-intercept, and the x-intercepts.
The x-coordinate of the vertex can be found using the formula "-b/2a", and the y-coordinate of the vertex can be found by substituting the x-coordinate of the vertex into the function for x.
The y-intercept is equal to "c", and the x-intercepts can be found by substituting a 0 into the function for f(x). Note that students are also asked to write the equation of the axis of symmetry of the given function, and find the domain, range, and maximum or minimum.
How to graph quadratic functions in standard form or vertex form?
The standard form of a quadratic function is
f(x) = a(x - h)2 + k, a ≠ 0
1. It is always a cup-shaped curve.
2. It opens upward if a > 0 and opens downward if a < 0.
3. The vertex is at (h, k) and the axis of the function is at x = h.
4. (h, k) is a maxima if a < 0 and a minima if a > 0.

Graphing Quadratic Functions in Standard Form (Vertex Form)



The Max and Min of a Quadratic Function
Graphing Quadratic Functions
Graph quadratic functions and find axis of symmetry, maximum or minimum, find domain and range.


 

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