All About Quadratic Functions!

6 Categories 30 Questions

The shape of a quadratic function. The lowest point on a parabola.

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Category 1

The shape of a quadratic function.

Parabola.

The lowest point on a parabola.

Minimum

The middle point of a parabola where the maximum/minimum is located

Vertex

Parabolas can be split down the middle and the left half is a perfect reflection of the right half. This property is called

Symmetry

The points where the graph crosses the x-axis

Solutions/Zeros/X-intercepts/Roots

Category 2

Formula for Standard Form of a Quadratic Function

Y = ax^2 +bx +c

The ___ value determines the direction the graph of a quadratic function opens.

The a value/coefficient

The _____ value is the y -intercept of the quadratic function in standard form.

The c value/constant

The formula for the axis of symmetry.

X =-b/2a

What is the relationship between the Axis of Symmetry and the vertex

The axis of symmetry runs through the vertex. So the x value is the same.

Category 3

What is the formula for vertex form of a quadratic function.

MULTIMEDIA

The h and k in vertex form give us what information about the quadratic function

The ordered pair (h,k) is the location of the vertex of the graph.

The equation x =h describes what in a quadratic function?

The axis of symmetry.

The formula for the factored form (intercept form) of a quadratic equation.

MULTIMEDIA

Factored allows us to easily identify what characteristics of a quadratic function?

The x-intercepts

Category 4

This graph opens up so the a value in standard form this quadratic function would be ....

Positive

What is the axis of symmetry for this graph?

X = 0.

What are the x - intercepts?

X = {-1, 1}

Identify the vertex and y intercept.

(3,0) and y=8

A quadratic function has a discriminant that is positive. Determine if this graph could represent that equation. Explain.

A positive discriminant would mean that the graph crosses the x axis twice. So this cannot be the graph.

Category 5

The first step when factoring a quadratic is to first look for a......

Greatest Common Factor!

What is the name of the factoring technique in the image called?

Difference of Squares

What is the name of the special trinomials in the picture?

Perfect Square Trinomials

Factor the expression.

(b-10)(b+3)

Factor the expression.

(2x+7)(x+6)

Category 6

Solve

V= {-6, 0}

Solve

K = {-6, -3}

Solve

X ={ -3, 3}

Solve using the Complete the Square Technique

A = {-5, 3}

Solve using the Quadratic Formula.

N = {-9, 15/2}

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