Transforming Quadratic Functions U3cL4

For the quadratic parent function f(x)=x^2, the axis of symmetry is ... the vertex is ... the zeros of the function are ...

axis of symmetry x=0 vertex (0,0) zeros of function: 1, x=0

different value of c same values of a and b

compare the coefficients of the following functions..

different vertex of the parabola same axis of symmetry x=0 same width of parabola

compare the graphs of the following functions..

Same axis of symmetry x=0 same vertex at (0,0) different widths of parabolas

compare the graphs of the following functions...

Order the functions from NARROWEST graph to WIDEST (note: find the absolute value of a) f(x) = -x^2 g(x) = 2/3x^2

f(x) = -x^2; abs value of a=1; narrower (a>1) g(x) = 2/3x^2; abs value of a = 2/3; wider (a<1)

Quadratic Parent Function

f(x)=x^2

Order the functions from NARROWEST graph to WIDEST (note: find the absolute value of a) f(x) = -4x^2 g(x) = 6x^2 h(x) = 0.2x^2

g(x) = 6x^2; abs value of a=6; narrower (a>1) f(x) = -4x^2; abs value of a=4; narrow (a>1) h(x) = 0.2x^2; abs value of a=0.2; wider (a<1)

The width of the parabola is narrower if

the absolute value of a greater than 1

The width of the parabola is wider if

the absolute value of a is less than 1

The value of a in a quadratic function determines not only the direction a parabola opens, but also

the width of the parabola

if c < 0, the graph of f(x)=x^2 + c is ....

translated c units down

if c > 0, the graph of f(x)=x^2 + c is ....

translated c units up

the graph of the function f(x)=x^2+c is the graph of f(x)=x^2 translated ..

vertically

linear parent function

y = x

different value of a same value of b and c

Compare the coefficients in the following functions.

The value of c in a quadratic function determines not only the value of the y-intercept but also

a vertical translation of the graph of f(x) = ax^2 up or down the y-axis