Wize High School Algebra I Textbook (Common Core) > Solving Quadratic Equations

Discriminant Analysis (Number of Solutions)

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Solutions From the Quadratic Formula
Recall that the quadratic formula is x=−b±b2−4ac2a\large x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac​​.

The b2−4acb^2-4acb2−4ac part is called the discriminant, and can help us easily determine the number of solutions a quadratic equation has!

Practice: Solutions from the Quadratic Formula
Determine the number of solutions in the following quadratic equations without solving the equation.

0=5x2−3x+70=5x^2-3x+70=5x2−3x+7

A) 0

B) 1

C) 2

I don't know

Practice: Solutions from the Quadratic Formula
Without graphing, determine if the vertex of each quadratic graph lies above, below, or on the x-axis.

a) y=−3x2−5x+8y=-3x^2-5x+8y=−3x2−5x+8

b) y=5x2−3x+6y=5x^2-3x+6y=5x2−3x+6

c) y=−x2+16x−64y=-x^2+16x-64y=−x2+16x−64

d) y=7x2−3x−4y=7x^2-3x-4y=7x2−3x−4

a) above / below / on

b) above / below / on

c) above / below / on

d) above / below / on

I don't know

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Practice: Solutions from the Quadratic Formula
Determine the value of the constant kkk such that the parabola y=7x2+8x−ky=7x^2+8x-ky=7x2+8x−k has 

a) no roots.

b) a single root.

c) 2 roots.

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