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# Sec 8: Solving Quadratic Equations with the Quadratic Formula - PowerPoint PPT Presentation

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.

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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

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 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 lets you know how many solutions there will be to a quadratic equation.

• You find the discriminant using the formula

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 price s at which each sweater is sold. The function

• HOME RUN worksheet

• Find the solutions using the quadratic formula