Finding sign of leading coefficient of a quadratic

Karlie Mays

Karlie Mays

Answered question

2022-04-08

Finding sign of leading coefficient of a quadratic equation
In a given quadratic equation f(x)=ax2+bx+c if f(1)4,f(1)<0 and f(3)>5, then how can I find the sign of a? Answer in the textbook: a>0.

Answer & Explanation

Vegljamzt6

Vegljamzt6

Beginner2022-04-09Added 16 answers

If f=0, then you have a straight line. Then
f(1)=f(1)+f(3)2>4+52=12>0
Then for a parabola with a>0 you have
f(x+y2)<f(x)+f(y)2
and for a<0 you have
f(x+y2)>f(x)+f(y)2
Since f(1)+f(3)2>0
and f(1)<0
then f(1+32)<f(1)+f(3)2

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