(HELP!) Can you please help me find the equation of this parabola? (concave down) (1 Viewer)

Jmmalic220 · Oct 19, 2016

Question 7 of Challenge 10 Maths in Focus (Preliminary Course)

Find the equation of the parabola with axis parallel to the y-axis and passing through points (0,-2), (1,0) and (3, -8).

I don't know how to do this problem, can anyone please show me working onto solving this?
Thank you very much in advance.

KingOfActing · Oct 19, 2016

Axis parallel to y-axis means it's vertical:

$y=ax^2+bx+c$

Substitute the three points and solve the resulting equations in 3 variables

Jmmalic220 · Oct 19, 2016

Thanks sir for quickly replying.

So, I got y = -2x, y = x^2 and y = 3x^2 - 8x

I've tried solving it but I got confused as to how to get this answer (provided by the book)
y = -2x^2 + 4x -2.

Can you please help me again? Thank you very much!

InteGrand · Oct 19, 2016

Jmmalic220 said:
Thanks sir for quickly replying.

So, I got y = -2x, y = x^2 and y = 3x^2 - 8x

I've tried solving it but I got confused as to how to get this answer (provided by the book)
y = -2x^2 + 4x -2.

Can you please help me again? Thank you very much!

$\noindent Let the equation be $y=ax^2 + bx+c$. Since $(0,-2)$ lies on the parabola, we have $c = -2$ ($y$-intercept). So $y=ax^2 + bx -2$. Sub. in $(1,0)$: $a+b-2 = 0$. Sub. in $(3,-8)$: $9a +3b-2 = -8$. Since $a + b-2=0$, we have $a = 2-b$. So $9a + 3b -2 = -8 \Rightarrow 9(2-b) + 3b = -6\Rightarrow 6b = 24 \Rightarrow b = 4$. Now, $a = 2-b = 2-4 = -2$. So the equation of the parabola is $y = -2x^2 + 4x-2$.$

Jmmalic220 · Oct 19, 2016

Thank you very much for this very good answer! I added reputation to you as well Sir!

InteGrand said:
$\noindent Let the equation be $y=ax^2 + bx+c$. Since $(0,-2)$ lies on the parabola, we have $c = -2$ ($y$-intercept). So $y=ax^2 + bx -2$. Sub. in $(1,0)$: $a+b-2 = 0$. Sub. in $(3,-8)$: $9a +3b-2 = -8$. Since $a + b-2=0$, we have $a = 2-b$. So $9a + 3b -2 = -8 \Rightarrow 9(2-b) + 3b = -6\Rightarrow 6b = 24 \Rightarrow b = 4$. Now, $a = 2-b = 2-4 = -2$. So the equation of the parabola is $y = -2x^2 + 4x-2$.$

Make a Difference – Donate to Bored of Studies!

(HELP!) Can you please help me find the equation of this parabola? (concave down) (1 Viewer)

Jmmalic220

New Member

KingOfActing

lukewarm mess

Jmmalic220

New Member

InteGrand

Well-Known Member

Jmmalic220

New Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)