Section 4.7 Complete the Square

California Standard: 8.0: Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. The also solve quadratic equations in the complex number system. 10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Solve quadratic equations by completing the square.

EXAMPLE 1: Solve .

COMPLETING THE SQUARE: TO COMPLETE THE SQUARE OF THE EXPRESSION , ADD THE SQUARE OR HALF THE COEFFICIENT OF , THAT IS ADD .

EXAMPLE 2: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

U-TRY#1: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial. a) c) b) 7

EXAMPLE 3: Solve by completing the square.

EXAMPLE 4: Solve by completing the square.

U-TRY#2: Solve the equation by completing the square. Leave your answer in radical form. a) c) b) 10

EXAMPLE 5: The area of a rectangle is 72 square units. Its width is x+2 and its length is 3x. What is the value of x?

Vertex Form: The vertex form of a quadratic function is where (h,k) is the vertex of the function’s graph.

EXAMPLE 6: Write in vertex form. Then identify the vertex.

EXAMPLE 7: The height y (in feet) of a baseball t seconds after it is hit is given by this function: Find the maximum height of the baseball.

HOMEWORK Sec 4.7 WS