How do you find the x and y intercepts for f(x) = -x^2 + 6x + 8?

1 Answer
Apr 26, 2017

x_("intercepts")-> -2 and -4

y_("intercept") =+8

Explanation:

Given:" "f(x)=-x^2+6x+8

The use of the term f(x) is that of giving a label (name) to a particular mathematical construct. The f is the name and the (x) bit means it is applied to x

So f(a) would mean: -a^2+6a+8
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color(blue)("Determine x-intercepts")

Observe that 2xx4=8" and that "2+4=6

so we can write: y=(x+2)(x+4)

The x-intercept is at y=0 so :

Set y=0=(x+2)(x+4)

Thus for this condition x=-2 and x=-4
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color(blue)("Determine y-intercept")

When the equation is in form y=ax^2+bx+c then

y_("intercept")=c=+8 color(red)(larr" Shortcut")

You obtain this value by substituting 0" for "x