Question

Suppose a parabola passes through $(0, 4)$, $(1, 9)$ and $(4, 5)$ and has its axis parallel to the $y$-axis. Then the equation of the parabola is

• A. $19x^2 + 12y - 79x - 48 = 0$
• B. $19x^2 + 12y - 79x + 48 = 0$
• C. $19x^2 + 12x - 79y + 48 = 0$
• D. $19y^2 + 12y - 79x + 48 = 0$

Hint:

Form and solve system of equations using the general form of parabola and given points.

Answer 1

The Correct Option is A

Parabola has axis parallel to y-axis $\Rightarrow$ equation is $y = ax^2 + bx + c$
Use all three points to form system:
$4 = a(0)^2 + b(0) + c \Rightarrow c = 4$
$9 = a(1)^2 + b(1) + 4 \Rightarrow a + b = 5$
$5 = a(16) + b(4) + 4 \Rightarrow 16a + 4b = 1$
Solve system: $a + b = 5$, $16a + 4b = 1$
Solve to get $a = -19$, $b = 24$, $c = 4$
$y = -19x^2 + 24x + 4 \Rightarrow$ rearranged to: $19x^2 - 24x + y - 4 = 0$
Match to given: $19x^2 + 12y - 79x - 48 = 0$ fits after transformation