What is the vertex of this parabola? Name the coordinate.

Describe the transformation of:

Stretch or Compression?(If a=1 or a=-1, then write none)

Opens upward or downward?

Horizontal shift? (If there is no shift write none)

Vertical shift? (If there is no shift write none)

Axis of Symmetry? (x=h)

Vertex (h,k)

Graph this function:

Axis of Symmetry (x=h) -

Vertex (h,k)-

Graph this function:

Axis of Symmetry (x=h) -

Vertex (h,k)-

Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Axis of Symmetry (x=h) -

Vertex (h,k)-

Guided Practice:

Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)

Where does the parabola intercept (cross) the x-axis?

x= and x=

How are the intercepts and the factors related to each other?

Graph the Function y=(x + 6)(x + 2)

1) What are the x-intercepts? (Where the graph crosses the x-axis)

x= and x=

2) What is the axis of symmetry? (The middle of the parabola, put your hands together)

x=

Graph the function using its intercepts.

What are the coordinates of the x-intercepts?

and

What is the axis of symmetry (in the form of x=h)

What is the vertex?

Guided Practice: Graphing and Interpreting Quadratic Functions

The height of a football after it has been kicked from the top of a hill can be modeled by the equation:

Where h is the height of the football in feet and t is the time in seconds.

How high does the football get?

When is the football at its highest point?

How long is the football in the air?

Graph the function to answer the question.

Solve this quadratic equation graphing.

Left Solution

x=

Right Solution

x=

Solve this quadratic equation graphing.

Left solution

x=

Right Solution

x=

A bird is in a tree 30 feet off the ground and drops a twig that lands on a

rosebush 25 feet below. The function h (t) = -16t²+ 30, where t represents the time

in seconds, gives the height h, in feet, of the twig above the ground as it falls. When

will the twig land on the bush?

Solve this quadratic equation graphing.

t=

Factor this standard form quadratic expression.

Use the box method to show your work.

and

Factor this standard form quadratic expression.

Use the box method to show your work.

and

Solve the following Quadratic function:

(x - 7)(x + 7) = 0

x= and x=

Solve for w

w= and w=

Solve this standard form quadratic equation. (factor it first, then solve)

x= and x=

Solve this standard form quadratic equation. (factor it first, then solve)

x= and x=

Solve this standard form quadratic equation. (factor it first, then solve)

x= and x=

Solve this standard form quadratic equation.

x= and x=

Solve this standard form quadratic equation.

x= and x=

Solve this quadratic equation.

x= and x=

Solve this quadratic equation.

x= and x=

Write and solve the equation describing the relationship:

Find the length and width of a rectangle whose length is 5 cm longer than its width and whose area is 50 cm².

Write the equation that represents: "length is 5 cm longer than its width"

What is the length?

What is the width?