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Graphs of Quadratic Functions

Intercepts, vertex, axis of symmetry, and forms of a quadratic.
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Graphs of Quadratic Functions
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Vocabulary

axis of symmetry

axis of symmetry

The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. The parabola is symmetrical about this line.
factored form

factored form

The factored form of a quadratic function f(x) is f(x)=a(x-r_{1})(x-r_{2}), where r_{1} and r_{2} are the roots of the function.
Intercept

Intercept

The intercepts of a curve are the locations where the curve intersects the x and y axes. An x intercept is a point at which the curve intersects the x-axis. A y intercept is a point at which the curve intersects the y-axis.
Intercepts

Intercepts

The intercepts of a curve are the locations where the curve intersects the x and y axes. An x intercept is a point at which the curve intersects the x-axis. A y intercept is a point at which the curve intersects the y-axis.
Maximum

Maximum

The maximum is the highest point of a graph. The maximum will yield the largest value of the range.
Maximum/Minimum

Maximum/Minimum

The maximum is the highest point of a function and the minimum is the lowest point of a function.
Minimum

Minimum

The minimum is the lowest point of a graph. The minimum will yield the smallest value of the range.
Parabola

Parabola

A parabola is the characteristic shape of a quadratic function graph, resembling a "U".
quadratic function

quadratic function

A quadratic function is a function that can be written in the form f(x)=ax^2 + bx + c, where a, b, and c are real constants and a\ne 0.
standard form

standard form

The standard form of a quadratic function is f(x)=ax^{2}+bx+c.
Transformations

Transformations

Transformations are used to change the graph of a parent function into the graph of a more complex function.
Vertex

Vertex

The vertex of a parabola is the highest or lowest point on the graph of a parabola. The vertex is the maximum point of a parabola that opens downward and the minimum point of a parabola that opens upward.
Vertex form

Vertex form

The vertex form of a quadratic function is y=a(x-h)^2+k, where (h, k) is the vertex of the parabola.

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