A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola.
knowing the vertex, you know that
y = a(x-7)^2 + 11
So, using the other point, just solve for a in
5 = a(3-7)^2+11
Well, it sounds like this parabola is taking a scenic route from (3,5) to (7,11). I wonder if it stopped for some ice cream along the way?
To find the equation of this parabola, we can use the vertex form, which is y = a(x-h)^2 + k.
The vertex of the parabola is given as (7,11), so that means h = 7 and k = 11.
Now we just need to find the value of a to complete the equation. To find a, we can use the fact that the parabola passes through the point (3,5).
So plugging in the coordinates (3,5) into the equation, we get:
5 = a(3-7)^2 + 11
Simplifying this equation, we get:
5 = a(-4)^2 + 11
5 = 16a + 11
Subtracting 11 from both sides, we have:
-6 = 16a
Dividing both sides by 16, we get:
a = -6/16
a = -3/8
So the equation of the parabola, in vertex form, is:
y = (-3/8)(x-7)^2 + 11
And there you have it! The parabola's equation with a sprinkle of humor.
To find the equation of the parabola in vertex form, we need to use the given point (3, 5) and the vertex (7, 11).
The vertex form of a parabola is given by: y = a(x-h)^2 + k, where (h, k) represents the vertex.
Step 1: Find the value of h and k (the vertex coordinates).
h = 7 (given)
k = 11 (given)
Step 2: Use the point (3, 5) to find the value of a.
Plug in the x and y values of the point into the vertex form:
5 = a(3-7)^2 + 11
Simplifying the equation:
5 = a(-4)^2 + 11
5 = 16a + 11
16a = 5 - 11
16a = -6
a = -6/16
a = -3/8
Step 3: Substitute the values of h, k, and a into the vertex form to get the equation.
y = a(x - h)^2 + k
y = (-3/8)(x - 7)^2 + 11
Therefore, the equation in vertex form that represents this parabola is:
y = (-3/8)(x - 7)^2 + 11
To find the equation of a parabola in vertex form, we need to know the coordinates of the vertex and one other point on the parabola.
The vertex form of a parabola is given by the equation: y = a(x-h)^2 + k, where (h, k) are the coordinates of the vertex.
Given that the vertex of the parabola is (7, 11), we have h = 7 and k = 11.
Now, we need to find the value of 'a', which is a constant that determines the shape and direction of the parabola. To obtain 'a', we can substitute the coordinates of the point (3, 5) into the equation.
Plugging in the values of x = 3 and y = 5 into the vertex form equation, we get:
5 = a(3 - 7)^2 + 11
Simplifying further:
5 = a(-4)^2 + 11
5 = 16a + 11
16a = -6
a = -6/16
a = -3/8
Now that we have the value of 'a', we can substitute it back into the vertex form equation to obtain the equation of the parabola:
y = (-3/8)(x - 7)^2 + 11
Therefore, the equation in vertex form that represents this parabola is y = (-3/8)(x - 7)^2 + 11.