Write equation of parabolla with vertex ( 4,3 ) passes through ( 5,2 ) vertical axis
perpendicular line to Y-axis passing through any point (m,n) is of the form
y=n
so the answer is
y=3
y:4
Y-k=4p(x-h)^
2-3=4p(5-4)^
-1=4p(1)^
-1-1=4p
4p=-2
P=-1/2 then the general equation will be
Y-3=-2(x-4)^
Tttttt
Well, well, well! We have a parabola in the house! Let's get down to business, shall we?
Since the vertex is given as (4,3), we know that the equation has the form:
y = a(x - h)^2 + k
where (h, k) represents the vertex. So, we can substitute in the given values:
y = a(x - 4)^2 + 3
Now, we also know that the parabola passes through the point (5,2). Let's use this juicy bit of information to solve for 'a'. Plugging in (5,2) into our equation, we get:
2 = a(5 - 4)^2 + 3
Simplifying that, we have:
2 = a(1)^2 + 3
2 = a + 3
To isolate 'a', we subtract 3 from both sides:
-1 = a
And there you have it, dear friend! The equation of the parabola is:
y = -1(x - 4)^2 + 3
Enjoy the beauty of parabolic laughter!
To find the equation of a parabola given its vertex and another point, you can use the vertex form of the equation. The vertex form of a parabola with a vertical axis is given by:
y = a(x - h)² + k
where (h, k) represents the coordinates of the vertex. In this case, the vertex is (4,3), so we have h = 4 and k = 3. The equation can be written as:
y = a(x - 4)² + 3
Now, we need to find the value of 'a' to determine the specific parabola passing through the given point (5,2). Plugging the coordinates of the point into the equation will help us to find 'a'.
2 = a(5 - 4)² + 3
2 = a(1)² + 3
2 = a + 3
a = 2 - 3
a = -1
Substituting the value of 'a' back into the equation, we get the final equation of the parabola:
y = -1(x - 4)² + 3
Therefore, the equation of the parabola with a vertical axis, vertex at (4,3), and passing through (5,2) is y = -1(x - 4)² + 3.