About Quadratic Functions

About Quadratic Functions

• are symmetric about a central line called the axis of symmetry

• ​the axis of symmetry intersects the parabola at the vertex

​Parabolas

• a ≠ 0

• Parent function: f(x) = x²

• type of graph: parabola (nonlinear)​

​f(x) = ax² + bx + c

Characteristics of Quadratic Functions

Some text here about the topic of discussion

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• the graph opens downward

• the highest point is called the maximum

• range: all real numbers less than or equal to the maximum​

​when a < 0

• the graph opens upward

• the lowest point is called the minimum

• range: all real numbers greater than or equal to the minimum​

​when a > 0

Characteristics of Quadratic Functions

The maximum or minimum is the vertex and the axis of symmetry cuts through the vertex.

Multiple Choice

What is the standard form of a quadratic equation?

• f(x)=x

• f(x)=x²

• f(x)=ax²+bx+c

• f(x)=a(x-h)²+k

Multiple Choice

What is the parent function of a quadratic equation?

• f(x)=x

• f(x)=x²

• f(x)=ax²+bx+c

• f(x)=a(x-h)²+k

Multiple Choice

What is a vertex?

• where the graph crosses the x-axis
• the y-intercept
• the maximum or minimum of the graph
• where the slope is vertical

Multiple Choice

How can you tell whether a parabola opens up or opens down by looking at the equation?

• The vertex tells you the direction of the opening

• The value of "a" tells you the direction of the opening.

• All parabolas open upward

• All parabolas open downward

Vertex:

​

Axis of sym:

​

y-int:​

​

​domain:

​

range:​​

Identify characteristics from graphs

​

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Plug in the axis of symmetry for x

​Vertex

Plug in a and b and solve.

Axis of Symmetry

y = 2x²+4x-3

Maximum or Minimum?

a < 1 a > 1​

Multiple Choice

$$y=-x^2+6x+4$$  

What is the axis of symmetry?

• 6

• -1

• -3

• 3

Multiple Choice

$$y=-x^2+6x+4$$  

What is the vertex?

• (3, 9)

• (3, 31)

• (-3, -23)

• (3, 13)

Multiple Choice

$$y=-x^2+6x+4$$  

Is the vertex a maximum or a minimum?

• Maximum

• Minimum

Multiple Choice

$$y=-x^2+6x+4$$  

What is the y-intercept?

• 3

• 4

• 10

• -3

• 2