8.3 Homework Graphing Quadratic Functions in Standard Form

The shape of the graph of a quadratic function is a

The factored form of a quadratic function is: {f(x) = }

The standard form of a quadratic function is: {f(x) =}

We know that the parabola opens upward when {a \gt} ; it opens downward when {a \lt} ;

If a parabola has a maximum value it opens ; if it has a minimum value it opens ;

In standard form, the value of the constant, {\bold c}, is also the on the graph.

In standard form, the 𝒙-coordinate of the vertex can be found using the formula{ x=} .

Graph {𝒚=𝟐𝒙^{𝟐}−𝟒𝒙−𝟑}

a: b: c:

{x= \frac{-b}{2a} =}

vertex: {\Large (},{\Large )}

y-intercept: {\Large (},{\Large )}

Axis of symmetry:

Domain: {\lt x \lt}

Range: {\le y \lt}

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Graph {𝒚=-𝟐𝒙^{𝟐}−8𝒙+1}

a: b: c:

{x= \frac{-b}{2a} =}

vertex: {\Large (},{\Large )}

y-intercept: {\Large (},{\Large )}

End Behavior:

{as \space x \rightarrow -\infty \space , \space y \rightarrow}

{as \space x \rightarrow -\infty \space , \space y \rightarrow}

Graph decreases: {\lt x \lt}

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