Sketch a graph of f(x)=-xsquared+3 and g(x)=10(x-4)squared. Please use two different axis.
Ok, so f(x) = -x^2 + 3 means that it is an INVERTED PARABOLA with the vertex at (0,3)
The x-intercepts are found by setting f(x) = 0
-x^2 + 3 = 0
x^2 = 3
x = +/- sqrt(3)
The graph looks like this:
Then we have g(x) = 10(x - 4)^2 which is parabola that is shifted to the right 4 units because of the (x - 4) term.
It has a y-intercept at g(0) = 10(0-4)^2 = 10(16) = 160
So the y-intercept is at (0, 160)
The x-intercept is where the vertex touches the x-axis
Again set g(x) = 0
10(x - 4)^2 = 0
x - 4 = 0
x = 4
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