Answer to Question #149355 in Algebra for Maricar

Question

Transformation in graph of quadratic equation

Objective: to analyzed the effect of changing the values of a,h,and k of a quadratic function and it's graph

Direction: to determine the transformation in the graph of an equation analyzed the effect of changing the values of a,h,and k in the graph of y=x²


1.y=5(x+9)²+11
2.y=-7(x-10)²+4

Answer 1

$y=5(x+9)^2+11$

1. $y_1=x^2$ black parabola

2. Shift the graph of $y_1=x^2$ to the left 9 units

$y_2=(x+9)^2$ blue parabola.

3. Stretch the graph $y_2=(x+9)^2$ vertically by factor of 5

$y_3=5(x+9)^2$ green parabola.

4. Shift the graph of $y_3=5(x+9)^2$ upward 11 units

$y_4=5(x+9)^2+11$ red parabola.

$y=-7(x-10)^2+4$

1. $y_1=x^2$ black parabola

2. Shift the graph of $y_1=x^2$ to the right 10 units

$y_2=(x-10)^2$ blue parabola.

3. Stretch the graph $y_2=(x-10)^2$ vertically by factor of 7

$y_3=7(x-10)^2$ green parabola.

4. Reflect the graph of $y_3=7(x-10)^2$ in the x-axis

$y_4=-7(x-10)^2$ orange parabola.

4. Shift the graph of $y_4=-7(x-10)^2$ upward 4 units

$y_5=-7(x-10)^2+4$ red parabola.