If (2, k) is a point on the parabola passing | vedclass

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(A) Let the equation of the parabola be $y = ax^2 + bx + c$ ... $(i)$Since the parabola passes through $(0, 2)$,we have $2 = a(0)^2 + b(0) + c$,so $c

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-$10$

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(A) Let the equation of the parabola be $y = ax^2 + bx + c$ ... $(i)$Since the parabola passes through $(0, 2)$,we have $2 = a(0)^2 + b(0) + c$,so $c = 2$.Since it passes through $(1, -3)$,we have $-3 = a(1)^2 + b(1) + 2$,which simplifies to $a + b = -5$ ... (ii)Since it passes through $(-1, 5)$,we have $5 = a(-1)^2 + b(-1) + 2$,which simplifies to $a - b = 3$ ... (iii)Adding equations (ii) and (iii),we get $2a = -2$,so $a = -1$.Substituting $a = -1$ into equation (ii),we get $-1 + b = -5$,so $b = -4$.Thus,the equation of the parabola is $y = -x^2 - 4x + 2$.Since $(2, k)$ lies on this parabola,we substitute $x = 2$ into the equation:$k = -(2)^2 - 4(2) + 2 = -4 - 8 + 2 = -10$.

If $(2, k)$ is a point on the parabola passing through the points $(1, -3), (-1, 5), (0, 2)$ and having its axis parallel to the $Y$-axis,then $k$ is equal to

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