Graph
g(x)=−6(x−2)(x)
Ok so I don't know how to do this because it isent two binomials but if you can help me this is what I got
Vertex:1,6
X-intercpts: x=2
Is that right if not explain it to me please!
g(x) = -6 x^2 + 12 x ... quadratic (parabola)
vertex is right
x-intercepts (zeroes) ... 2 and 0
you did pretty good for not knowing...
Thanks Scott!
To graph the equation g(x) = -6(x-2)(x), you can start by finding the x-intercepts and the vertex.
1. X-intercepts:
To find the x-intercepts, we need to solve g(x) = 0. Set the equation to zero:
-6(x-2)(x) = 0
Now, we have two factors (-6), (x−2), and (x). For the product to be zero, at least one of these factors must be zero. Therefore, we can set each factor equal to zero separately:
a) -6 = 0 (this is not possible since -6 is not equal to zero)
b) x-2 = 0 (solve for x)
x = 2
So, the only x-intercept is x = 2.
2. Vertex:
To find the vertex of the parabola, we can rewrite the equation g(x) in the standard form: g(x) = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
g(x) = -6(x-2)(x)
= -6(x^2 - 2x)
= -6x^2 + 12x
Now, we can complete the square to rewrite the equation in vertex form:
g(x) = -6(x^2 - 2x + ?) - ?(?)
= -6(x^2 - 2x + 1) - (-6)(1)
= -6(x^2 - 2x + 1) + 6
From the expression (x^2 - 2x + 1), we can recognize it as a perfect square trinomial, which factors as (x-1)^2. Therefore, we can rewrite the equation as:
g(x) = -6(x-1)^2 + 6
Comparing the equation with the vertex form, we can see that the vertex of g(x) is (1, 6). Therefore, your answer is correct.
So, the graph of g(x) will have a vertex at the point (1, 6) and an x-intercept at x = 2.