Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form. (1 point) Responses y = (x – 5)2 – 3 y = ( x – 5) 2 – 3 y = 4(x – 5)2 – 3 y = 4( x – 5) 2 – 3 y = 4(x + 5)2 – 3 y = 4( x + 5) 2 – 3 y = 4(x – 5)2 + 3
The correct equation of the parabola in vertex form is:
y = (x – 5)² – 3
To write the equation of the parabola in vertex form, we need to use the vertex and a point on the parabola.
Given that the vertex is (5, -3) and the point is (6, 1), we can substitute these values into the vertex form equation.
The vertex form equation is y = a(x - h)^2 + k, where (h, k) represents the vertex.
Substituting h = 5 and k = -3 into the equation, we have:
y = a(x - 5)^2 - 3
Now we can substitute the coordinates of the given point (6, 1) into the equation to find the value of 'a'.
1 = a(6 - 5)^2 - 3
1 = a(1)^2 - 3
1 = a - 3
a = 1 + 3
a = 4
Plugging the value of 'a' back into the equation, we have:
y = 4(x - 5)^2 - 3
Therefore, the equation of the parabola in vertex form is y = 4(x - 5)^2 - 3.
To write the equation of the parabola in vertex form, we need to use the vertex form equation of a parabola: y = a(x-h)^2 + k, where (h, k) represents the vertex.
Given that the vertex is (5, -3), we can substitute these values into the vertex form equation: y = a(x-5)^2 - 3.
Now, we know that the parabola also passes through the point (6, 1). To find the value of 'a', we can substitute this point into the equation and solve for 'a'.
1 = a(6-5)^2 - 3
1 = a(1)^2 - 3
1 = a - 3
a = 4
Substituting the value of 'a' back into the vertex form equation, we get our final equation: y = 4(x-5)^2 - 3.
Therefore, the correct equation of the parabola in vertex form is y = 4(x-5)^2 - 3.