SEC 8 SOLVING QUADRATIC EQUATIONS WITH THE QUADRATIC

SEC 8: SOLVING QUADRATIC EQUATIONS WITH THE QUADRATIC FORMULA Learning Target: Students will solve quadratic equations using the quadratic formula in mathematical and real-world situations and use the determinant to determine how many solutions there will be> Homework: Home. Run worksheet

Standard Form of a Quadratic Equation Ax² + Bx + C = 0 Ex 1: Write the quadratic equation. (a) A= 2, B = 3, C = -5 2 x² + 3 x – 5 = 0 (b)A= 1, B = -4, C = 8 x² - 4 x + 8 = (c)A = -5, B = 0, C = 250 -5 x² + 25 = 0

The QUADRATIC FORMULA The Quadratic Formula will find all x-values in any quadratic equation. On a graph, these would be the x-intercepts (zeros, roots). *In order for the quadratic formula to work, the equation MUST EQUAL 0!

The Discriminant � # of Solutions Positive 2 zero 1 Negative None (or non-real)

Ex 1: Quality Core Practice According to this determinant, how many solutions will this quadratic equation have?

Finding Solutions to Quadratic Equations Equation 3 x² -5 x - 2 = 0 Fill in the Quadratic Formula What is the How Many Discriminant? Solutions? Work & Solutions

Ex 3: The profit P from handmade sweaters depends on the price s at which each sweater is sold. The function P = -s² + 120 s – 2000 models the monthly profit from sweaters for one custom tailor. Find how much the company should charge for each sweater in order to break even.

HOMEWORK � HOME RUN worksheet � Find the solutions using the quadratic formula