Vocabulary Terms - Quadratics

Front 1

What are zeros of a function? How do you find them?

Back 1

For a function f(x), the zeros are the x values when f(x)=0. To find the zeros set the function rule equal to zero and solve for x.

Front 2

What are the roots of function?

Back 2

The roots of a function are the x values that make ax^2+bx+c=0.

Front 3

How do you solve a quadratic equation?

Back 3

There are three methods we've learned so far:
1. Factor & use zero product property.
2. Take square roots
3. Complete the square

Front 4

What is vertex form of a quadratic? Where is the vertex?

Back 4

F(x)=a(x-h)^2+k

Vertex is the point (h, k)

Front 5

What is standard form, and what are the 4 properties of a quadratic in standard form?

Back 5

F(x)=ax^2+bx+c
4 properties:
1. Opens up if a>0, down if a<0
2. axis of symmetry is x=-b/2a
3. Vertex is (-b/2a, f(-b/2a))
4. Y-intercept is c

Front 6

How do you go from vertex form to standard form of a quadratic equation?

Back 6

Expand the square, and combine like terms.

Front 7

How do you go from standard form to vertex form?

Back 7

Use completing the square:
1. Group variable terms
2. Factor a, if needed
3. Add (b/2)^2 to the variable terms and subtract a(b/2)^2 from the constant
4. Write the trinomial as perfect square, and combine the constant terms.

Front 8

What are the six steps to complete the square?

Back 8

1. Put variable terms on one side of the equation and constants on the other.
2. Divide by a if needed
3. Complete the square by adding (b/2)^2 to both sides of the equation.
4. Write trinomial as a perfect square
5. Take square roots of both sides. Remember +\- roots.
6. Solve for x.

Front 9

When solving application problems, what are the two parts of a parabola that you would need to find?

Back 9

Maximum/minimum value and zeros

Front 10

What is (a + b)^2?

Back 10

A^2 + 2ab + b^2

Front 11

What is (a-b)^2?

Back 11

A^2 - 2ab + b^2