y = - 5(x + 1)^2 + 6
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
the x- coordinate of the vertex lies on the axis of symmetry and the maximum value is the y-coordinate of the vertex, hence
vertex = (- 1, 6 )
y = a(x + 1)² + 6
To find a substitute (- 2, 1) into the equation
1 = a + 6 ⇒ a = - 5
y = - 5(x + 1)² + 6 ← equation in vertex form
The equation of the parabola in vertex form is y = - 5(x + 1)² + 6.
The vertex form of a parabola is y = a(x - h)² + k.
Here, (h, k) are the coordinates of the vertex and 'a' is the coefficient.
Here, x = -1.
Therefore, the x- coordinate of the vertex will lie on the symmetry axis.
Again, y- coordinate of the vertex indicates the value of 'k' that indicates from the function (x - h) = 0.
Therefore, the vertex of the parabola = (- 1, 6 )
Therefore, the equation of the parabola in vertex form:
y = a(x - h)² + k
⇒ y = a(x + 1)² + 6
Now, if we put the point (-2, 1) through which the parabola passes, then we will get the value of 'a'.
Therefore,
1 = a (- 2 + 1)² + 6
⇒ a + 6 = 1
⇒ a = - 5
Therefore, the required equation of the parabola in vertex form will be:
y = - 5(x + 1)² + 6
Learn more about equation of the parabola in vertex form here: https://brainly.com/question/2348714
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