Question

For the quadratic function f(x)=2x ² −8x+2,which of the following statements is correct regarding its vertex, y-intercept, and direction?

A) Vertex: (2,−6), Y-intercept: (0,2), Opens upwards.
B) Vertex: (−2,6), Y-intercept: (0,2), Opens upwards.
C) Vertex: (2,6), Y-intercept: (0,2), Opens downwards.
D) Vertex: (−2,−6), Y-intercept: (0,2), Opens downwards.

Answer 1

The vertex of the quadratic function f(x)=2x^2 - 8x + 2 is (2, -6), the y-intercept is (0, 2), and the quadratic opens upwards. A) Vertex: (2,−6), Y-intercept: (0,2), Opens upwards.

Step-by-step explanation:

The quadratic function f(x) = 2x^2 - 8x + 2 has a vertex, y-intercept, and direction. To find the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. Plugging in the values from the function, we get x = -(-8) / (2(2)) = 2. Substituting this value back into the function, we find the y-coordinate of the vertex: f(2) = 2(2)^2 - 8(2) + 2 = -6.

The vertex of the function is therefore (2, -6).

To find the y-intercept, we can set x = 0 in the function and solve for y: f(0) = 2(0)^2 - 8(0) + 2 = 2.

The y-intercept of the function is therefore (0, 2).

Lastly, to determine the direction of the quadratic, we look at the coefficient of x^2. Since the coefficient is positive (+2), the quadratic opens upwards.