what is the vertex and axis of symmetry
y=2x^2 - 7x + 1
Y = 2x^2 - 7x + 1.
V(h , k),
h = Xv = -b / 2a,
= 7 / 4 = 1 3/4.
Substitute 7/4 for x in the given Eq:
k = Yv = 2(7/4)^2 - 7(7/4) +1,
= 98/16 - 49/4 +1,
= 49/8 - 49/4 + 8/8,
= 49/8 - 98/8 + 8/8,
= - 41/8 = -5 1/8.
V(1 3/4 , - 5 1/8).
Axis of Sym. = h = Xv = 1 3/4.
To find the vertex and axis of symmetry of the quadratic function y = 2x^2 - 7x + 1, we can use the formula:
x = -b / (2a)
where a, b, and c are the coefficients of the quadratic function in the standard form ax^2 + bx + c. In this case, a = 2, b = -7, and c = 1.
Step 1: Find the x-coordinate of the vertex using the formula x = -b / (2a).
Plug in the values of a and b into the formula:
x = -(-7) / (2 * 2)
x = 7 / 4
Step 2: Substitute the x-coordinate of the vertex into the quadratic function to find the y-coordinate.
Plug in x = 7 / 4 into the original function:
y = 2(7 / 4)^2 - 7(7 / 4) + 1
y = 2(49 / 16) - 49 / 4 + 1
y = 98 / 16 - 196 / 16 + 1
y = -98 / 16 + 1
y = -98 / 16 + 16 / 16
y = -82 / 16
y = -41 / 8
Therefore, the vertex of the quadratic function is (7/4, -41/8).
Step 3: Find the axis of symmetry.
The axis of symmetry is always a vertical line passing through the x-coordinate of the vertex, in this case, x = 7/4.
Therefore, the axis of symmetry for the given quadratic function is x = 7/4.
To find the vertex and axis of symmetry of a quadratic equation in the form of y = ax^2 + bx + c, you can use the following formulas:
1. Vertex formula:
The x coordinate of the vertex (h) can be found using the formula h = -b / (2a), and the y coordinate (k) can be found by substituting the x coordinate back into the equation.
2. Axis of symmetry formula:
The axis of symmetry is a vertical line that passes through the vertex, and its equation can be found using the formula x = -b / (2a).
Now, let's apply these formulas to your equation y = 2x^2 - 7x + 1:
1. Vertex formula:
In this equation, a = 2, b = -7, and c = 1.
To find the x coordinate of the vertex (h):
h = -b / (2a)
h = -(-7) / (2*2)
h = 7 / 4
To find the y coordinate of the vertex (k), substitute the x coordinate back into the equation:
k = 2(7/4)^2 - 7(7/4) + 1
k = 49/8 - 49/4 + 1
k = 49/8 - 98/8 + 8/8
k = -49/8
Therefore, the vertex is (7/4, -49/8).
2. Axis of symmetry formula:
The axis of symmetry is given by x = -b / (2a):
x = -(-7) / (2*2)
x = 7 / 4
Hence, the axis of symmetry is x = 7/4.
So, for the equation y = 2x^2 - 7x + 1, the vertex is (7/4, -49/8) and the axis of symmetry is x = 7/4.