Equations

Question 1

How can a quadratic equation be derived from its roots?

Answer 1

negative sum of roots: b

product of roots: c

Question 2

What is the discriminant, and what does it mean?

Answer 2

The discriminant, used for quadratic equations, is equal to: b^2 -4ac

positive discriminant: there are two real solutions, and two distinct x-intercepts on the graph
when the discriminant is zero: there is one (repeated) real solution, and one x-intercept on the graph
when the discriminant is negative: there are two complex solutions, and there are no x-intercepts on the graph

Question 3

State the quadratic formula.

Answer 3

x = (-b±√(b^2-4ac))/2a

Question 4

What is the process checklist for solving a quadratic equation?

Answer 4

Also note that while the discriminant is cannot determine roots, it can be useful when solving.

1. Greatest Common Factor
2. Grouping
3. Square Root Method
4. Completing the Square
5. Quadratic Formula

Question 5

What is a quadratic equation in standard form?

Answer 5

f(x) = a(x - h)2 + k

Question 6

How can you find the vertex of a quadratic equation in two steps?

Answer 6

First, use the equation x = f (-b/2a) to find the x-value of the vertex

next, plug that back into the equation to find the y-value of the vertex