Graphing Quadratics in Vertex Form

4.2 - Quadratics in Standard Form

Section 4.2

Objective

To graph quadratic functions written in standard form.

Axis of Symmetry

The axis of symmetry is a vertical line through the vertex of the function's graph.

Equation of the axis of symmetry

Multiple Choice

What is the axis of symmetry of the graph of

$$y=\left(x+2\right)^2-3$$  ?

• $$\left(-2,\ -3\right)$$  

• $$x=2$$  

• $$x=-2$$  

• $$x=-3$$  

Multiple Choice

What is the axis of symmetry of the graph pictured here?

• $$x=4$$

• $$x=-4$$

• $$\left(-4,\ -1\right)$$

• $$y=x^2+8x+15$$

Properties of a parabola

Open Ended

Determine the vertex of the of the graph of

$$f\left(x\right)=\ x^2-6x+8$$  

Multiple Choice

Graph the function

$$y=x^2-x-6$$  

Solutions To A Quadratic Equation

The solutions to a quadratic equation are th epoints at which the function intersects the x-axis.
The solutions are referred to as zeros, roots, or x-intercepts.

Minimum and Maximum Values

• When a parabola opens upward, the y-value of the vertex is the minimum value.

• When a parabola opens downward, the y-value of the vertex is the maximum value.

Open Ended

Determine the maximum value of the function

$$y=-2x^2-2x+4$$  

Converting from Standard Form To Vertex Form

Open Ended

Write the equation in Vertex form

y = -2x²-8x-4

Open Ended

Write the equation in Vertex form

y = x²-2x-35

Open Ended

A baseball is thrown from an initial height of 6 ft. The height

$$h$$  of the baseball can be modeled by  $$h\left(t\right)=-16t^2+50t+6$$  where  $$t$$  is the time in seconds since the ball was thrown. Approximately how many seconds does it take the ball to reach its maximum height? What is the maximum height that the ball reaches?