Intro to Solving Quadratic Equations

What are the zeros?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

What is another word for roots of an equations?

(Select all choices that apply.)

• y-intercepts
• zeros

• vertex
• x-intercepts

• solutions

What are the steps to solving this by completing the square?

x² + 10x + 21 = 0

• Subtract 21 from both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

• Take the square root of both sides of the equation

• Subtract 5 from both sides of the equation

Answer explanation

Steps for completing the square when a=1

1st: Rewrite as x² + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

​Complete the quadratic formula in the diagram shown given that a quadratic equation is in

standard form

ax² + bx + c = 0,

a

b

c

Solve by the Square Root method: x² = 16

• ± 4

• ± 8

• 4i

• 8i

• -4i

The points at which a parabola intersects the x-axis are the ________________.

• quadratic roots

• vertex

• axis of symmetry

• asymptotes

• factors

How many solutions are in the graph of the quadratic equation shown?

• 0

• 1

• 2

• 3

The ____________ is used to determine the number of solutions to a quadratic equation.

If the discriminant is positive, d ​ (a)   0, then there are ​ (b)   real solutions.

If the discriminant is zero, d ​ (c)   0, then there is ​ (d)   real solution.

If the discriminant is negative, d ​ (e)   0, then there are no real solutions.

• >
• 2
• =
• 1
• <
• 0
• 3
• ≧
• ≦

Order the following steps for solving quadratic equations by factoring.

• Set the quadratic equation equal to zero.

• Factor the left side.

• Set each factor equal to zero, and solve each for the variable.

• Write the answer using curly braces in set notation.