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anonymous
 one year ago
WILL FAN AND MEDAL :) Plz help me walk through this!
Functions f(x) and g(x) are described as follows:
f(x) = 2x^2 + 3
x g(x)
0 0
1 2
2 3
3 2
4 0
anonymous
 one year ago
WILL FAN AND MEDAL :) Plz help me walk through this! Functions f(x) and g(x) are described as follows: f(x) = 2x^2 + 3 x g(x) 0 0 1 2 2 3 3 2 4 0

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which statement best compares the maximum value of the two functions? It is equal for both functions. It is 2 units higher for f(x) than g(x). It is 2 units lower for f(x) than g(x). It is 1 unit higher for f(x) than g(x).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Concentrationalizing @sammixboo

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@amistre64 @TheSmartOne

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@billj5 can you help me? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so the part I'm having trouble with is finding the maximum of f(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x) is a quadratic. The graph of a quadratic is a parabola, which would either have a finite minimum value or a finite maximum value. In this case you have a finite maximum value (because the question implies this and because the leading coefficient is negative). Given a quadratic with a general form of \(ax^{2} + bx + c = 0\), the xcoordinate of the maximum or minimum value is equal to \(b/2a\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this might help http://www.purplemath.com/modules/fcntrans.htm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Have you seen the b/2a idea before, horse?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok thank you @billj5 ;)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes I have :) @Concentrationalizing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, awesome. So for our problem, what is b/2a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think it would be 3/2(2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Actually, it would be 0. Note that the b in the general form is the coefficient of the x to the first power variable. Yet our equation has no x to the first power, we only have an x^2 and a constant term. Thus b is 0, which makes b/2a = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I meant those would be the values. So would the 3/2(2) = 0?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0b is not 3, though, b is 0. Since a quadratic is \(ax^{2} + bx + c\), a is what goes with the x^2 term. So a for us is 2. b is what goes with the x term. But our equation is 2x^2 + 3, we dont have an x term. Thus b has to be 0. Then our constant, c, is 3. So a = 2, b = 0, c = 3. Which means b/2a = 0/2(2) = 0/4 = 0 Does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But f(x) only has two terms?`:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it's not a quadratic `:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A quadratic is any function in which all the powers are integers and the highest power is a 2. So all of these would be quadratics: \(x^{2} + 5x + 6\) \(\frac{3x^{2}}{5}  9\) \(x^{2}\) The first has 3 terms, the 2nd has 2, the last one has 1 term. But they're all quadratics because all of the exponents are integers and the highest one is a 2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok but I still don't get why b = 0.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433381836170:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433381878344:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ooooh! That makes sense ;)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would all just equal 0. Got it :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol, glad the visual helped. But yes, b is 0 because that part is missing :3 So that means the xcoordinate of the maximum value is 0. So since we need x to be 0, we can just plug in 0. If we plug in 0, we get \(2(0)^{2} + 3 = 0 + 3 = 3\) Thus the maximum value is 3 for f(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Got it! That makes total sense now. I guess I must be a visual person lol :3 Thanks again @Concentrationalizing !
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