Answer:
In order from smallest to largest:
g(x)=(1,-2)
now, f(x) and h(x) would reach the same height, so from left to right on the graph, if plotting all vertices:
h(x)=(-2,2)
f(x)=(4,2)
Explanation:
f(x)
f(x)=-2(x-4)^2+2
This is the vertex form of a quadratic equation: The formula used is f(x)=a(x-h)^2+k, where (h,k) is the vertex. In this case, 4 is h and 2 is k, so the vertex of this equation is (4,2).
g(x)
g(x)=5x^2-10x+7
To find the vertex of a quadratic equation in standard form, you first have to find the x-coordinate of the vertex using the formula, -b/2a. In this equation, a=5 and b=-10, so plug into the formula: -(-10)/2(5)=10/10=1, so the x-coordinate of the vertex is 1. Now to find the y-coordinate of the vertex by plugging in the x-coodinate for x in the equation: 5(1)^2-10(1)+7=5(1)-10+7=5-10+7=-5+7=-2, so your y-coordinate is -2. Therefore, your vertex for this equation is (1,-2).
h(x)
So, this quadratic function is in the form of a graph. The vertex of the graph is the maximum of minimum value of the graph, depending on whether the graph is positive or negative. In this graph, it is the maximum point, which is (-2,2).