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Kindly help me with this question..This isn't homework, i am just trying to work through problems as i am helping my son with his maths as he is disadvantage.

I have done most of the questions but i am stuck with question 2.4. So the assistance would really be appreciated...

I have attached a picture regarding the question as the link doesn't work.

You know from solving question 2.1 that the vertex of the parabola is D(-1, 4).

Find the distance d between A(-3, 0) and D(-1, 4):

rise = 4 - 0 = 4

run = -1 - (-3) = 2

By the Pythagorean Theorem,

d² = rise² + run² = 4² + 2² = 20

d = √20 = 2√5

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Equation for circle of radius r, centered at (h, k):

(x-h)² + (y-k)² = r²

So the equation for the circle of radius 2√5, centered at A(-3, 0) is:

(x+3)² + y² = 20

https://www.flickr.com/photos/dwread/14593721683/

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Question 2.6

You already know from solving questions 2.1 and 2.2 that

f(x) = -x² - 2x + 3

g(x) = 2x + 6

Let u(x) = f(x) - g(x) = -x² - 4x - 3.

When u(x) is a maximum, u'(x) = 0

u'(x) = -2x - 4 = 0

x = -2

u(-2) = -(-2)² - 4(-2) - 3 = 1

The maximum vertical distance between f and g is 1.

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