# Thread: concerning the graphs of a function

1. ## concerning the graphs of a function

f(x)= 1/4(x-2)^2-4

how can the parabola that is the graph of f be obtained from the graph of y=x^2

what are the co-ordinates of the vertex of the parabola?

what are the x-intercepts and the y-intercepts of the parabola?

what is the image set of the function in interval notation?

2. ## Graphical interpretation of Transformation of a function

Hello loes
Originally Posted by loes
f(x)= 1/4(x-2)^2-4

how can the parabola that is the graph of f be obtained from the graph of y=x^2
The graph of $f(x - a)$ is the graph of $f(x)$ shifted to the right $a$ units.

The graph of $kf(x)$ is the graph of $f(x)$ stretched parallel to the $y$-axis with factor $k$.

The graph of $f(x) - b$ is the graph of $f(x)$ shifted downwards $b$ units.

Put these three facts together, and you can describe how the graph of $y=\tfrac{1}{4}(x-2)^2 - 4$ is obtained from the graph of $y = x^2$.

what are the co-ordinates of the vertex of the parabola?
Where is the vertex of $y = x^2$? So where will it end up when you apply all three of these transformations?

what are the x-intercepts and the y-intercepts of the parabola?
The $x$-intercepts are the values of $x$ that satisfy $\tfrac{1}{4}(x-2)^2 - 4=0$.

The $y$-intercept is the value of $y$ when $x = 0$.

what is the image set of the function in interval notation?
What is the image set for $y = x^2$? What will happen to this set when the transformations are applied?