Find the maximum value of g if g(x) = 7-8x-2x^2
I assume you are in calculus. If not, find the point halfway between the roots (factor it), and use that x to calculate g.
g'= -8+4x=0 x=2
so max g is 7-16-8= check that.
Well, the maximum value of g can be found by considering the quadratic equation. You know, math can be quite quadratic, just like a slow and repetitive dance. Shall we sway into it together?
For the given quadratic equation g(x) = 7 - 8x - 2x^2, we need to find the best flight for g to reach its peak. By best flight, I mean the maximum value of g.
Now, in order to find the maximum value, we should look at the coefficient of the x^2 term, which is -2. As it's negative, it suggests that the parabola will be facing downside, like a dreary frown that needs some clown-induced laughter.
So, let's try to turn that frown upside down, shall we? To find the maximum point, we can use the vertex formula: x = -b/2a.
Plugging in the given values for b and a (b = -8 and a = -2), we get x = -(-8) / (2 * -2). Now, solving this equation may look like trying to untangle a bunch of clown wigs, but trust me, it's not as complicated as it seems.
After simplifying the equation, we find x = 1. Substituting this value back into g(x), we get g(1) = 7 - 8(1) - 2(1^2) = -3.
So, the maximum value of g is -3. It seems like g has hit a bit of a humorous low point. But don't worry, my clownish friend, we can always turn things around and bring joy back into our mathematical circus!
To find the maximum value of g(x), we need to find the vertex of the parabola represented by the function g(x) = 7 - 8x - 2x^2.
The vertex of a parabola in the form of g(x) = ax^2 + bx + c is given by the formula x = -b/(2a).
In this case, a = -2 and b = -8. Thus, x = -(-8)/(2*(-2)) = 8/(-4) = -2.
To find the maximum value of g(x), substitute x = -2 into the function g(x).
g(-2) = 7 - 8(-2) - 2(-2)^2
= 7 + 16 - 8
= 23 - 8
= 15.
Therefore, the maximum value of g is 15.
To find the maximum value of the function g(x) = 7 - 8x - 2x^2, we can follow these steps:
Step 1: Rewrite the equation in standard form:
g(x) = -2x^2 - 8x + 7
Step 2: Identify the coefficient of x^2. In this case, it is -2, which is negative. Since the coefficient is negative, we know that the parabola will open downwards, and therefore, the vertex will represent the maximum value.
Step 3: Determine the x-coordinate of the vertex. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = -2 and b = -8, so the x-coordinate of the vertex is:
x = -(-8) / (2 * -2) = 8 / (-4) = -2
Step 4: Find the corresponding y-coordinate of the vertex. We substitute the x-coordinate into the equation to get the value of g(x):
g(-2) = -2(-2)^2 - 8(-2) + 7
= -2(4) + 16 + 7
= -8 + 16 + 7
= 15
Therefore, the maximum value of g(x) is 15.