What are the vertex and the axis of symmetry of the equation?
y = –2x2 + 8x – 18
(1 point)
Responses
vertex: ( 2, –10)
axis of symmetry: x = 2
vertex: ( 2, –10) axis of symmetry: x = 2
vertex: (2, –10)
axis of symmetry: x = –10
vertex: (2, –10) axis of symmetry: x = –10
vertex: (–2, –10)
axis of symmetry: x = –2
vertex: (–2, –10) axis of symmetry: x = –2
vertex: (–2, 10)
axis of symmetry: y = –2
The correct response is:
vertex: (2, –10)
axis of symmetry: x = 2
The correct response is:
vertex: (2, -10)
axis of symmetry: x = 2
To find the vertex and axis of symmetry of the equation y = –2x^2 + 8x – 18, you can use the formula x = -b / 2a for the x-coordinate of the vertex.
In the equation y = –2x^2 + 8x – 18, a = -2 and b = 8.
Using the formula x = -b / 2a, substitute the values of a and b:
x = -8 / (2 * -2)
x = -8 / -4
x = 2
So, the x-coordinate of the vertex is 2.
To find the y-coordinate of the vertex, substitute the value of x back into the equation:
y = –2(2)^2 + 8(2) – 18
y = –2 * 4 + 16 – 18
y = -8 + 16 - 18
y = -2
Therefore, the vertex of the equation is (2, -2).
The axis of symmetry is a vertical line that passes through the x-coordinate of the vertex. So, in this case, the axis of symmetry is x = 2.
Therefore, the correct answer is:
vertex: (2, -2)
axis of symmetry: x = 2