Introduction to the Quadratic Formula

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 - 4ac

-7

What is the value of the discriminant for the quadratic equation 0 = 2x2 + x - 3? Discriminant = b2 - 4ac

25

Which is the graph of a quadratic equation that has a positive discriminant?

NOT B

What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 = 0?

NOT a = -2, b = 4, c = 3

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

The discriminant is −4, so the equation has no real solutions.

Which best explains why the expression cannot be rewritten as during the next step?

The square root of terms separated by addition and subtraction cannot be calculated individually.

What are the values of a, b, and c in the quadratic equation 0 = x2 - 3x - 2?

a = , b = -3, c = -2

Some of the steps in the derivation of the quadratic formula are shown. Step 3: -c + = a Step 4a: -c + = a Step 4b: + = a Which best explains or justifies Step 4b?

converting to a common denominator