 # Completing the Square and the Quadratic Formula

## Presentation on theme: "Completing the Square and the Quadratic Formula"— Presentation transcript:

Completing the Square and the Quadratic Formula
Objective: To solve quadratic equations by completing the square and using the quadratic formula.

Completing the Square When completing the square, we follow the same technique each time.

Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other.

Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2.

Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2. Take half of the middle term and square it.

Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2. Take half of the middle term and square it. Add that number to both sides.

Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2. Take half of the middle term and square it. Add that number to both sides. Solve

Completing the Square Solve:

Completing the Square Solve: Add eight to both sides.

Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides.

Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides. Solve.

Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides. Solve.

You Try Solve

You Try Solve

You Try Solve

Completing the Square Solve:

Completing the Square Solve: Subtract 3 from both sides

Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2

Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2 Take half of 4, square it, add to both sides

Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2 Take half of 4, square it, add to both sides Complete the square

Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2 Take half of 4, square it, add to both sides Complete the square Take the square root and solve.

Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2 Take half of 4, square it, add to both sides Complete the square Take the square root and solve.

You Try Solve

You Try Solve

You Try Solve

Vertex Form After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

Vertex Form After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

Example 4

Example 4

We can solve it using the quadratic formula:

Set the equation equal to zero.

Set the equation equal to zero. a=1, b=3, c=-9

Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

You Try Solve using the quadratic formula.

You Try Solve using the quadratic formula.
Set the equation equal to zero. a=1, b=-3, c=-7 Use the quadratic equation.

Axis of Symmetry The axis of symmetry for a parabola is the vertical line This is also the x coordinate of the vertex. Put this back into the equation to find the y coordinate of the vertex.

Example 4

Example 4

You Try Write the equation for the axis of symmetry and the vertex for the following.

You Try Write the equation for the axis of symmetry and the vertex for the following.

You Try Write the equation for the axis of symmetry and the vertex for the following.

Homework Page 304 17-45 odd Page 311 11-33 odd