Question

Consider the function ( g(x) = 4x^2 - 16x + 7 ).

a) What is the vertex?

b) What is the axis of symmetry?

Answer 1

The vertex of the function is (2, -9) and the axis of symmetry is x = 2.

Step-by-step explanation:

The given function is a quadratic function in the form of y = ax^2 + bx + c, where a = 4, b = -16, and c = 7.

a) To find the vertex, we can use the formula x = -b/(2a) to find the x-coordinate and then substitute it into the function to find the y-coordinate. Plugging in the values, we have x = -(-16)/(2*4) = 2. Substituting this value back into the function, we get y = 4(2)^2 - 16(2) + 7 = -9. Therefore, the vertex is (2, -9).

b) The axis of symmetry is a vertical line passing through the vertex. In this case, the equation of the axis of symmetry is x = 2.