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:

graph1.png

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

graph2.png

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