Question #5fd61

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Question #5fd61

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Answer 1 · 2017-02-06T15:52:46

y-intercept = 8
x-intercepts:
$x = \frac{7 \pm \sqrt{17}}{2}$ $x = (7 +- sqrt17)/2$

Explanation:

$f (x) = x^{2} - 7 x + 8$ $f(x) = x^2 - 7x + 8$
To find y-intercept, make x = 0
x = 0 --> y-intercept --> f(0) = 8
To find x-intercepts, make y = 0, and solve this quadratic equation by using the improved quadratic formula (Socratic Search):
$x^{2} - 7 x + 8 = 0$ $x^2 - 7x + 8 = 0$
$D = d^{2} = b^{2} - 4 a c = 49 - 32 = 17$ $D = d^2 = b^2 - 4ac = 49 - 32 = 17$ --> $d = \pm \sqrt{17}$ $d = +- sqrt17$
There are 2 real roots (two x- intercepts):
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{7}{2} \pm \frac{\sqrt{17}}{2} = \frac{7 \pm \sqrt{17}}{2}$ $x = -b/(2a) +- d/(2a) = 7/2 +- sqrt17/2 = (7 +- sqrt17)/2$

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Question #5fd61

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