Find the vertex and axis of symmetry of y = -2x^2 + 4x + 1. Show all of your work and justify your reasoning.
Note: The ^ symbol means to the power.
Y = -2x^2 + 4x + 1.
Xv = h = -b/2a = -4 / -4 = 1.
In the given Eq, substitute 1 for x:
Yv = k = -2*1^2 + 4*1 +1 = 3.
V(h,k) = (1,3).
Axis: X = h = 1.
To find the vertex and axis of symmetry of the quadratic function y = -2x^2 + 4x + 1, we can use the formula:
x = -b / (2a)
where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c.
In this case, a = -2 and b = 4. Let's calculate the value of x using the formula:
x = -4 / (2(-2))
x = -4 / (-4)
x = 1
The x-coordinate of the vertex is 1.
To find the y-coordinate of the vertex, substitute this value of x into the equation:
y = -2(1)^2 + 4(1) + 1
y = -2 + 4 + 1
y = 3
Therefore, the vertex is (1, 3).
The axis of symmetry is a vertical line that passes through the vertex. The equation of the axis of symmetry can be written as x = a, where a is the x-coordinate of the vertex.
In this case, the axis of symmetry is x = 1.