Warm Up Using the quadratic formula find the zeros of the following:

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Presentation transcript:

Warm Up Using the quadratic formula find the zeros of the following: 1. x2 – 9x + 12 = 0 2. x2 + 4x – 16 = 0 3. 2x2 + 8x – 13 = 0

Answers Using the quadratic formula find the zeros of the following: 1. x2 – 9x + 12 = 0 x = 7.37, x = 1.63 2. x2 + 4x – 16 = 0 x = 2.47, x = -6.47 3. 2x2 + 8x – 13= 0 x = 1.24, x = -5.24

discriminant

Create a rough sketch of the following quadratic functions Create a rough sketch of the following quadratic functions. How many times does each quadratic touch the x-axis? 1. 2. 3.

The discriminant determines how many solutions a quadratic function will have.

If the discriminant is POSITIVE, there are 2 REAL solutions. If the discriminant is ZERO, there is 1 REAL solution If the discriminant is NEGATIVE, there are 2 IMAGINARY solutions.

Find the discriminant for each quadratic equation. 1. 2. 3.

Given the following quadratics, use the discriminant to determine how many solutions it will have. 1. x2 – 6x + 11 = 2 2. 3x2 + 5x = 12 3. 3x2 + 48 = 0 4. x2 – 27 = 0 5. x2 + x + 1 = 0 6. x2 + 4x -1 = 0

Given the following graphs of a quadratic function: Determine the sign of the discriminant. Determine whether the solutions are real or imaginary.