Maths Quadratic Question -Please help :D

[Keshuv19]

Hey guys , please help me i have been trying to answer this question since yesterday and my answer is 5 can you please confirm it.

Given that g (0) = 5 and 2 is the axis of symmetry, find g (4). (Hint: there are 3 ways in which a quadratic can be solve).

Edited June 30, 2013 by Keshuv19

[SurajM]

Yes the answer is 5 because this a parabola which is equidistant from the axis of symmetry.

[maroctam]

As an extension to this question and out of pure curiosity, would it be possible to find g(3) given the information above and the coordinates of the vertex? (say, (2,2) for example?)

Edit: I just thought about this, and realised that it can be solved rather easily using simultaneous equations. Sorry, that was a pointless question! (for those who are interested, here's the answer.)

Edit 2: I didn't see that -._._.- has kindly answered before my first edit.

Edited June 30, 2013 by naweln

[-._._.-]

you know the general formula for a quadratic is

y = ax² + bx + c
c is 5 because that is the y-intercept (when x is 0, y = 5)

From the Maths SL and HL (and further maths SL) booklet, the axis of symmetry is when x = -b/2a

so 2 = -b/2a
b = -4a -------------- Equation 1

Another equation:

when x = 2, y=2

2 = (a)2² + b(2) + 5
2 = 4a + 2b + 5 ---------- Equation 2

Substitute Equation 1 into Equation 2:
2 = 4a + 2(-4a) + 5
2 = 4a -8a +5
4a = 3
a = 3/4 ----------- Equation 3

Substitute Equation 3 into Equation 1:
b = -4(3/4)
b = -3

so quadratic formula:
y = 3/4 x² - 3 x + 5

if we use f(x) notation:

f(x) = 3/4 x² - 3x + 5

f(3) = 27/4 - 9 + 5 = 27/4 - 4 = 11/4

Edited June 30, 2013 by -._._.-