(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 $y = -2x^2 + 4x-2$.$

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

Jmmalic220

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KingOfActing

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InteGrand

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