Graph of a parabola

Question

enter image description here The equation of the following graph is $-x^2-4x-c=y$ how to find c if 3OB=AO

What is your own attemps? Say, when you put $x = 0$, $y = ?$ — GNUSupporter 8964民主女神地下教會, Feb 08 '18 at 18:04
I think the parabola it's a graph of a quadratic function. What is it "graph of parabola"? — Michael Rozenberg, Feb 08 '18 at 18:09

score 2 · Answer 1 · answered Feb 08 '18 at 18:13

2

Let $A(x_2,0)$ and $B(x_1,0).$

Thus, $$x_1x_2=c,$$ $$x_1+x_2=-4$$ and $$3x_1=-x_2,$$ which gives $$x_2=-6,$$ $$x_1=2$$ and $$c=-12.$$

answered Feb 08 '18 at 18:13

Michael Rozenberg

194,933

james watt · Answer 2 · 2018-02-08T18:35:59.810

1

Finding the roots you get $$-2\pm\sqrt{4-c}$$ then you know $$x_A=-2-\sqrt{4-c}$$$$x_B=-2+\sqrt{4-c}$$ then you need to have $x_B>0 \implies c<0$ so you need to solve $|x_A|=3x_B$ $$2+\sqrt{4-c}=3(-2+\sqrt{4-c})$$ that give you $$c=-12$$

edited Feb 08 '18 at 18:35

answered Feb 08 '18 at 18:12

james watt

644
3
11

score 1 · Answer 3 · answered Feb 08 '18 at 18:40

1

Slight variation of previous answer: $$y=-x^2-4x-c=-(x-A)(x-B)=-(x-(-3B))(x-B)=-x^2-2Bx+3B^2$$ Equating the coefficients: $$-4=-2B \Rightarrow B=2; c=3B^2=12.$$

answered Feb 08 '18 at 18:40

farruhota

31,482

Graph of a parabola

3 Answers3