Question

Solve each equation by completing the squar 5 0=x² +12x+11 6. 27=3x² +12x 7. 0=2x² +6x-14 Write the equation in vertex form, and identi the maximum or minimum value of the graph

Answer 1

To solve each equation by completing the square, divide the equation by the coefficient of the squared term and format it in the form a(x+b)^2+c=0. Find b/2, square it to get c, and subtract c from both sides. Simplify the equation and identify the maximum or minimum value of the graph based on the sign of the coefficient of the squared term.

Step-by-step explanation:

To solve each equation by completing the square:

1. First, make sure that the coefficient of the squared term is 1. If it's not, divide the equation by that coefficient.
2. Format the equation in the form a(x+b)^2+c=0.
3. Now, find the value of b/2 and square it to get c.
4. Subtract c from both sides of the equation.
5. Simplify and write the equation in vertex form.
6. Identify the maximum or minimum value of the graph based on the sign of the coefficient of the squared term.

An example of applying this method would be:

For equation 5: x² + 12x + 11 = 0

1. Divide the equation by 1 to get: x² + 12x + 11 = 0
2. Complete the square by adding (12/2)^2 = 36 to both sides: x² + 12x + 36 + 11 = 36
3. Write the equation in vertex form: (x+6)^2 = -47
4. Here, the coefficient of the squared term is positive, so the graph reaches its minimum value. The minimum value can be found by evaluating the constant term, which is -47 in this case.

Follow a similar process for equations 6 and 7 to find their vertex form and determine the maximum or minimum value of their graphs.