Find the coordinates of the midpoint for the following equation: y = -2x^2 + 20x + 1.
Your answer should be in the form (x-coordinate, y-coordinate).
(Hint: Find the x-coordinate by using the Midpoint Formula [-b / (2a)]. Then find the y-coordinate by plugging the x-coordinate value into the original equation and solving for “y.”)
How do I even begin???
y = -2x^2 + 20x + 1
I will help with this but for the other two just look at them
What happens for huge negative x?
What happens for huge positive x?
for this one follow directions
-b/2a = -20/-4 = 5
that means that the graph of this parabola crosses the x axis equal distance left and right of x = 5
so your axis of symmetry is x = 5
Now for the y value of the vertex, just solve using x = 5
y =-2(5)^2 + 20*5 + 1
To find the coordinates of the midpoint for the given equation, we can follow these steps:
Step 1: Identify the coefficients of the equation.
Looking at the equation y = -2x^2 + 20x + 1, we have:
a = -2 (coefficient of x^2)
b = 20 (coefficient of x)
c = 1 (constant term)
Step 2: Find the x-coordinate using the Midpoint Formula.
The x-coordinate of the midpoint can be found using the formula: x = -b / (2a)
Substituting the coefficients, we have:
x = -20 / (2 * -2)
x = -20 / -4
x = 5
So, the x-coordinate of the midpoint is 5.
Step 3: Find the y-coordinate by plugging the x-coordinate into the original equation.
Now that we have the x-coordinate (which is 5), we can find the y-coordinate by substituting it into the original equation and solving for y.
Plugging in x = 5 into the equation y = -2x^2 + 20x + 1, we get:
y = -2(5)^2 + 20(5) + 1
y = -2(25) + 100 + 1
y = -50 + 100 + 1
y = 51
So, the y-coordinate of the midpoint is 51.
Therefore, the coordinates of the midpoint for the given equation y = -2x^2 + 20x + 1 are (5, 51).