Answer:
The axis of symmetry of the parabola with a vertex at (-3, 2) is at
x = -1/2
Step-by-step explanation:
Given a quadratic function (parabola) of the form:
y = ax² + bx + c
The axis of symmetry of the function is a vertical line that divides the parabola into two congruent halves. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
This is given as x = -b/2a
We are given a parabola with vertex at (-3, 2). The quadratic function corresponding to this is
y = (x -(-3))(x - 2)
= (x + 3)(x - 2)
= x² - 2x + 3x - 6
y = x² + x - 6
Here, a = 1, b = 1, and c = -6
The axis of symmetry is at
x = -b/2a
= -1/2(1)
= -1/2
The axis of symmetry of the given parabola should be [tex]y-2=m(x+3)[/tex] for all cases. And, for horizontal and vertical orientation, the equation of the axis of symmetry should be y=2 and x=-3, respectively.
Given information:
The parabola has vertex at (-3,2).
It is required to get the axis of the parabola.
In general, the parabola with vertex (3,2) can have any axis of symmetry based on the orientation of the parabola. The only condition is that the axis must pass through the point (3,2).
The general equation of the axis of symmetry with slope m (orientation) should be,
[tex]y-(2)=m(x-(-3))\\y-2=m(x+3)[/tex]
So, the general equation of the axis of symmetry of the given parabola should be [tex]y-2=m(x+3)[/tex].
In normal cases, the orientation of the parabola is either horizontal or vertical.
In case of vertical orientation, the slope should be infinite or 1/0. So, the equation of axis will become,
[tex]0(y-2)=(x+3)\\x=-3[/tex]
In case of horizontal orientation, the slope should be infinite or 1/0. So, the equation of axis will become,
[tex](y-2)=0(x+3)\\y=2[/tex]
Therefore, the axis of symmetry of the given parabola should be [tex]y-2=m(x+3)[/tex] for all cases. And, for horizontal and vertical orientation, the equation of axis of symmetry should be y=2 and x=-3, respectively.
For more details, refer to the link:
https://brainly.com/question/23290624
