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How do you find the x and y intercepts for $f (x) = x^{2} - 9 x + 14$ $f(x)=x^2-9x+14$ ?

1 Answer

Jan 20, 2016

y-intercept: $14$ $14$
x-intercepts: $2$ $2$ and $7$ $7$

Explanation:

Note that $y$ $y$ is equivalent to $f (x)$ $f(x)$
So we can think of the given equation as
$XXX y = x^{2} - 9 x + 14$ $color(white)("XXX")y=x^2-9x+14$

The y-intercept is the value of $y$ $y$ when $x = 0$ $x=0$ .
Given the form of the equation above, clearly:
$XXX$ $color(white)("XXX")$ y-intercept $= 14$ $=14$

The x-intercept(s) is/are the value(s) of $x$ $x$ for which $y = 0$ $y=0$
$XXX x^{2} - 9 x + 14 = 0$ $color(white)("XXX")x^2-9x+14=0$

$\to X (x - 7) (x - 2) = 0$ $rarrcolor(white)("X")(x-7)(x-2)=0$

That is $x = 7$ $x=7$ or $x = 2$ $x=2$

$XXX$ $color(white)("XXX")$ x-intercepts: $= 7$ $=7$ and $2$ $2$

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