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To determine the maximum value of a quadratic function opening downwards, we are going to find the vertex; then the y-value of the vertex will be our maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
we'll use the vertex formula: 
, and then we are going to replace that value in our original function to find k.
So, in our function
, 
and 
.
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of
is (2,1), and for the graph we can tell that the vertex of 
is (-2,4). The only thing left is compare their y-coordinates to determine w<span>hich one has the greater maximum value. Since 4>1, we can conclude that </span> has the greater maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
So, in our function
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, - 8) ← 2 points on the line
m = =
= - 4
The line crosses the y- axis at (0, 0) ⇒ c = 0 , then
y = - 4x + c , that is
y = - 4x → A