# 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 $\displaystyle f(x - a)$ is the graph of $\displaystyle f(x)$ shifted to the right $\displaystyle a$ units.

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

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

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

what are the co-ordinates of the vertex of the parabola?
Where is the vertex of $\displaystyle y = x^2$? 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 $\displaystyle x$-intercepts are the values of $\displaystyle x$ that satisfy $\displaystyle \tfrac{1}{4}(x-2)^2 - 4=0$.

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

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