How do you find the axis of symmetry, vertex and x intercepts for y=−x2−3x+4?

1 Answer
salamat · MathFact-orials.blogspot.com
Jul 18, 2017

axis of symmetry is x=−32
vertex minimum at 254
x-intercepts are (1,0)and(−4,0)

Explanation:

y=−x2−3x+4

to find axis of symmetry and vertex, we can use completing a square to solve it.

y=−(x2+3x)+4

y=−(x+32)2+(32)2+4

y=−(x+32)2+94+164

y=−(x+32)2+254 →i

it axis of symmetry can be found when (x+32)=0, then x=−32

since −(x+32)2 is always has a -ve value, therefore it has a maximum vertex at 254

to find x-intercepts, plug in y=0 in →i

0=−(x+32)2+254

(x+32)2=254

(x+32)=±√254

x=−32±52

x1=−32+52=22=1

x2=−32−52=−82=−4

therefore x-intercepts are (1,0)and(−4,0)

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