Test Math

What happens to the parent function if the absolute value of the leading coefficient is greater than 1?

>1 gets narrower <1 gets wider

What formula do you use to find the axis of symmetry?

x=-b/2a

What point on the graph does the c represent in the standard from of a quadratic equation?

y-intercept

What is the standard from of a quadratic equation?

y=ax^2+bx+c

What is the parent function of a quadratic?

y=x^2

How do you determine if the graph will open up or down?

+ will open down - will open up

y-intercept

The value of the output when the input is zero. The location where the graph of a function touches the y-axis.

The x-intercept are also called:

-roots -zero -solutions

List two ways to graph a quadratic function:

-t-table -vertex and AOS -vertex

What shape is the graph of a quadratic function?

A U-shaped graph

Quadratic Function

A function whose input is squared. This means there will be two inputs that yield the same output.

Rational Number

A number that can be written as a quotient of two integers.

Square Root

A number that when multiplied by itself equals a given number.

No Solutions (quadratic)

A quadratic function that does not have an x-intercept. There are NO REAL solutions, but there are 2 COMPLEX solutions. The discriminant is a negative value.

One Solution (quadratics)

A quadratic function that has one x-intercept. The discriminant has a value of zero. This indicates that the zero is repeating or is said to have a multiplicity of 2.

Two Solutions (quadratic)

A quadratic function that has two x-intercepts. The discriminant is a positive value.

Parabola

A symmetrical curve formed by a quadratic function.

Axis of Symmetry

A vertical line (x=a) that divides a parabola into two symmetrical halves.

When you factor a quadratic equation, where do you plot the zero, solutions, or roots?

on the x-axis

Vertex: (1, 4) Axis of Symmetry: x = 1

Find the axis of symmetry for the given equation

x-intercepts: 9, -3 Average of x-intercepts: (9+-3)/2 = 3 Axis of Symmetry: x = 3

Find the axis of symmetry for the given equation

For any graph, the y-intercept is where the x-value is equal to 0. Thus, letting x = 0, and solving for y, we would get 0. Therefore, the y-intercept is 0. OR For a quadratic function in standard form, the y-intercept is always the value of c. In this instance c= 0. Therefore, the y-intercept is 0

Find the y-intercept of the quadratic function

1. Find the x-coordinate of the vertex, x = -b/2a. 2. Plug the x-coordinate of the vertex into the original equation to find the coordinate of the y-value. 3. The maximum/minimum value is the y-value, or you can give me the ordered pair.

How do you find maximum/minimum value of a quadratic function that is in standard form?

The vertex is opposite h and k. (-h, k)

How do you find the vertex of a quadratic function in vertex form?

1. Find the axis of symmetry 2. Find the vertex 3. Find any point by plugging an x-value into the given function. 4. Reflect the point you found in step 3 over the axis of symmetry. 5. Sketch the graph

How do you graph a quadratic function?

1. You could set one side of the equation equal to 0 & factor. 2. You could complete the square.

How would you solve for x?

1. Find the x-intercepts 2. Find the average of the x-intercepts (add them and divide by 2) 3. Your answer from step 2 is gives you the EQUATION of the line for the axis of symmetry, x = (average of the 2 x-intercepts)

If the quadratic function is in Intercept Form, how do you find the Axis of Symmetry?

Use the equation x=-b/2a. The axis of symmetry is the LINE x = _______

If the quadratic function is in standard form, how do you find the Axis of Symmetry?

The parabola has a maximum (The graph is a frown)

In a quadratic function, if the a value is negative, does the graph have a minimum or maximum?

Minimum (he is a smile)

In a quadratic function, if the a value is positive, does the graph have a minimum or maximum?

The graph will be wider (stretched)

In a quadratic function, if the value of a is a fraction less than one, will the the graph wider or more narrow than the graph of y = x^2?

It will be more narrow.

In a quadratic function, if the value of a is greater than one, will the the graph wider or more narrow than the graph of y = x^2?

In solving for x, you are finding the values of x that, when plugged back into the original equation, make a TRUE statement. (e.g. plugging 2 in for x in the original equation gives you the true statement, 72=72. Also, plugging -9 back into the original equation, gives you the true statement, 72=72) In solving for x, you are also finding the x-coordinates of the points of intersection of the parabola, 4x²+28x and the line, y=72.

In the equation below, what does it mean to solve for x?

What is the vertex? How do you know if it is a maximum or minimum value?

It is the lowest or highest point of parabola

What happens to the graph of the parent function is the leading coefficient is negative?

It opens down

How do you know a function is a quadratic function?

It will have a x^2

What happens to the parent graph if a constant is added or subtracted?

It will move the parabola up or down

Quadratic Formula

Method used to find the x-intercepts (solve) a quadratic equation that cannot be factored.

Irrational Number

Non-repeating, non-terminating decimal numbers. Examples: pi and the square root of 2

Factors

Numbers or expressions that are being multiplied to form a product. [Ex: 2 x 6 = 12 or (x-3)(x+2) = x²-x-6 ]

Discriminant

The expression under the radical sign in the quadratic formula. It indicates the number and the type (rational, irrational, complex) of solutions a quadratic function will have.

Vertex

The input that yields the minimum or maximum output value of a quadratic function. Turning point on a parabola and where the axis of symmetry is located.

What is the axis of symmetry?

The line passing through the vertex that divides the parabola into 2 symmetric parts.

Radical

The number of times the radicand is multiplied by itself.

Intercept Form

The product of two expressions. a = dilation (p, 0) & (q, 0) = x-intercepts

Standard Form

The quadratic function shown is in what form?

x-intercepts (zeros, roots, solutions)

The value of the input when the output is zero. The location where the graph of a function touches the x-axis. (4 terms for the same thing)

y=ax²+bx+c

What is Standard Form of a Quadratic Function?

y=(x-p)(x-q)

What is the Intercept Form of a Quadratic Function?

A parabola

What is the name of the graph of a quadratic function?

y= a(x-h)²+k

What is vertex form of a quadratic function?

A, C, D, F, G, I, J and L (for each of these functions, the greatest exponent is 2)

Which of the following functions are quadratic functions?

How do you find the vertex?

You substitute the AOS into the equation

Vertex Form

a = dilation (h, k) = coordinate of vertex

Standard Form

a = dilation c = y-intercept (0, c)