Question

Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.

Answer 1

Answer:

Choice B: $y = 2\, (x - 6)^{2} + 5$.

Step-by-step explanation:

For a parabola with vertex $(h,\, k)$, the vertex form equation of that parabola in would be:

$\text{ y = a\, (x - h)^{2} + k for some constant a }$.

In this question, the vertex is $(6,\, 5)$, such that $h = 6$ and $k = 5$. There would exist a constant $a$ such that the equation of this parabola would be:

$y = a\, (x - 6)^{2} + 5$.

The next step is to find the value of the constant $a$.

Given that this parabola includes the point $(7,\, 7)$, $x = 7$ and $y = 7$ would need to satisfy the equation of this parabola, $y = a\, (x - 6)^{2} + 5$.

Substitute these two values into the equation for this parabola:

$7 = (7 - 6)^{2}\, a + 5$.

Solve this equation for $a$:

$7 = a + 5$.

$a = 2$.

Hence, the equation of this parabola would be:

$y = 2\, (x - 6)^{2} + 5$.