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

​

Fill in the Blanks

What is the vertex of this parabola?

Fill in the Blanks

What is the axis of symmetry of this parabola?

Fill in the Blanks

What is the y-intercept of this parabola?

Fill in the Blanks

What is the domain of this parabola?

Fill in the Blanks

What is the range of this parabola?

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