Algebra vocab chapter 10

Algebra vocab chapter 10

This is a quadratic

• Also know as a parabola

• Enter the equation into your calculator and graph

Vertex

• Vertex is the turning point

• In this case it is a minimum

• If the a term was negative it would be a maximum

• (1,4)

Fill in the Blanks

What is the vertex of this graph

Enter in coordinate form

Axis of symmtry

• The line where I could fold the parabola and the sides would line up

• formula  $x=-\frac{b}{2a}$  

• In this example x=1

Fill in the Blanks

What is the axis of symmetry of this graph

Roots

• Where graph crosses x axis or when y=0

• (-1,0) and (3,0)

Fill in the Blanks

What are the roots of this graph

Enter the coordinates from left to right

Parent graph

• The original shape

• We would describe other graphs in the graph family relative to this graph

 $y=x^{2\ }+1$  

• Vertical shift up 1

•  $y=x^2+k$  would move k units up and  $y=x^{2\ }-k$  would move k units down

 $y=\left(x+2\right)^2$  

• Horizontal shift left 2

•  $y=\left(x+h\right)^2$  would move h left up and  $y=\left(x-h\right)^2$  would move h units right

Vertex form

•  $y=a\left(x-h\right)^2+k$  

• (h,k) is the vertex

• Find the left/right shift from h

• Find the up/down shift from k

• Find the vertical stretch from a

• If a is negative it is reflected over y-axis

Multiple Choice

What is the vertex form of this parabola?

• $y=\left(x-1\right)^2-4$

• $y=\left(x+1\right)^2-4$

• $y=\left(x-1\right)^2+4$

• $y=\left(x+1\right)^2+4$

Open Ended

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