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: HomeRun worksheet
Standard Form of a Quadratic Equation Ax² + Bx + C = 0 • Ex 1: Write the quadratic equation. • (a) A= 2, B = 3, C = -5 • 2x² + 3x – 5 = 0 • A= 1, B = -4, C = 8 • A = -5, B = 0, C = 25 • -5x² + 25 = 0 • x² - 4x + 8 = 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 • The discriminant lets you know how many solutions there will be to a quadratic equation. • You find the discriminant using the formula
Ex 1: Quality Core Practice According to this determinant, how many solutions will this quadratic equation have?
Ex 3: The profit P from handmade sweaters depends on the price s at which each sweater is sold. The function P = -s² + 120s – 2000models 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