What is the vertex and p-value of this parabola?
1 answer:
Answer:
- vertex: (-7, 5)
- p = 2
Step-by-step explanation:
The vertex is halfway between the focus and the directrix:
((-7, 7) +(-7, 3))/2 = (-14, 10)/2 = (-7, 5) . . . . vertex coordinates
The value of p is the distance from the focus to the vertex:
7 -5 = 2 = p
In vertex form, the equation of the parabola is ...
y = 1/(4p)(x -h)^2 +k . . . . . . vertex (h, k)
y = 1/8(x +7)^2 +5
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Answer:
Step-by-step explanation:
The exponent rule that applies to products like this is ...
... (a^b)(a^c) = a^(b+c)
In your problem, this is
... x^(1/3)·x^2 = x^(1/3 +2) = x^(1/3 +6/3) = x^(7/3)
This fractional exponent translates to the root of a power:
... = (x^7)^(1/3)
In typeset form, it is ...
You have already figured correctly that the coefficient is 3·8 = 24.