<h3>
Answer: a = 9</h3>
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Explanation:
Vertex form in general is
y = a(x-h)^2 + k
The given vertex is at (3,6) meaning (h, k) = (3, 6)
So h = 3 and k = 6 are plugged into the first equation shown above
y = a(x-h)^2 + k
y = a(x-3)^2 + 6
Now plug in x = 1 and y = 42, which is from (x,y) = (1,42).
So we get,
y = a(x-3)^2 + 6
42 = a(1-3)^2 + 6
At this point, we have one variable and we can isolate it like so:
42 = a(1-3)^2 + 6
42 = a(-2)^2 + 6
42 = a(4)
42 = 4a+6
4a+6 = 42
4a = 42-6
4a = 36
a = 36/4
a = 9 is the final answer
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Extra info (optional section):
This means the y = a(x-h)^2 + k becomes y = 9(x-3)^2 + 6
Let's expand that out and get it into standard form
y = 9(x-3)^2 + 6
y = 9(x^2-6x+9) + 6
y = 9x^2-54x+81+6
y = 9x^2 - 54x + 87
The last equation is in the form y = ax^2+bx+c where,
a = 9
b = -54
c = 87
