The standard form of hyperbola is:
(x-h)²/a²-(y-k)²/b²=1
center:(4,5)
Length of the horizontal transverse axis: 8-5=3=2a
thus
a=3/2
a²=9/4
b=2
b²=4
Hence the equation will be:
(x-4)²/(9/4)-(y-5)²/4=1
simplifying this we get:
[4(x-4)²]/9-(y-5)²/4=1
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The answer is C. Hope that helps
Answer:
f(x) = 6x² - 24x + 21
Step-by-step explanation:
The equation of a quadratic function in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (2, - 3 ) , then
f(x) = a(x - 2)² - 3
To find a substitute (1, 3 ) into the equation
3 = 1(1 - 2)² - 3
3 = a(- 1)² - 3
3 = a - 3 ( add 3 to both sides )
6 = a
f(x) = 6(x - 2)² - 3 ← in vertex form
= 6(x² - 4x + 4) - 3
= 6x² - 24x + 24 - 3
f(x) = 6x² - 24x + 21 ← in standard form
He would maybe have 7.5 but I insist you the answer could be 8 too
