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The point where the parabola crosses the y-axis is called the y-intercept.

The y-intercept is (0, 4).

Parabola opening up, vertex (4,-4)

The point(s) where the parabola crosses the x-axis is called the x-intercept.

Other names for the x-intercepts are roots, zeros, and solutions.

The x-intercepts are (-2, 0) and (2, 0).

Parabola opening up, vertex ((0,-4)

Notice that some parabolas have 2 x-intercepts.

Some parabolas only have 1 x-intercept.

Parabola opening up, vertex (-3,0)

And some parabolas have no x-intercepts.

Parabola opening up, vertex (3,4)

On your graph paper, draw a parabola that has no x-intercepts and a vertex of (-2, 4)?

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Name the y-intercept and the zero(s) for the given graph.

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y-intercept: (0, -4)
zeroes or x-intercepts: (1, 0) and
(5, 0)

Parabola opening down, vertex (3,4)

Think about a quadratic function that has a vertex of (2, -5) and a y-intercept of (0, -2). Sketch the graph and then describe its characteristics.

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Parabola opening up, vertex (2,-5)

Here are some descriptions you may have included:

The parabola is facing up since vertex is below the y-intercept.
The graph will have one positive and negative x-intercept.
The axis of symmetry is x = 2 since the x-coordinate of the vertex is 2.
The vertex in this graph is also the minimum point.

Extra Practice Problems

Think about a quadratic function that has x-intercepts of (1, 0) and (-5, 0) and a y-intercept of (0, 3). Sketch the graph and then describe its characteristics.

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Parabola opening down, vertex (-2,6)

Here are some descriptions you may have included:

The parabola is facing down since the y-intercept is above the x-intercepts.
The axis of symmetry is x = -2 since -2 is half way between 1 and -5.
The vertex is also the maximum since it is the highest point.

Think about a quadratic function that has no roots (x-intercepts) and a vertex of (3, 2). Sketch the graph and then describe its characteristics.

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Your graph should be similar to one of the following.

Parabola opening up

Here are some descriptions you may have included:

The parabola is facing up since the vertex is above the x-axis and there are no x-intercepts.
The axis of symmetry is x = 3 since the x-coordinate of the vertex is 3.
The y-intercept is a positive value since the graph is facing up.