Question

Find the vertex of the given quadratic function.

Answer 1

To find the vertex of a quadratic function, calculate the x-coordinate using -b/(2a) from the standard equation form ax²+bx+c=0, and then substitute this x-value into the function to obtain the y-coordinate.

Step-by-step explanation:

To find the vertex of a quadratic function, we can use the standard form of a quadratic equation, which is ax²+bx+c = 0. For a function in this form, the x-coordinate of the vertex is found using the formula -b/(2a), and once we have the x-coordinate, we can substitute it back into the original quadratic function to find the corresponding y-coordinate.

For example, if we have a quadratic function f(x) = 4.90x² - 14.3x - 20.0, the x-coordinate of the vertex would be -(-14.3)/(2*4.90). This gives us approximately 1.458. We would then substitute x = 1.458 back into the function to get the y-coordinate, completing the coordinates of the vertex.

Answer 2

B

given f(x) in factored form, equate to zero for x-intercepts

(x - 8)(x - 4) = 0, hence

x = 4, x = 8 ← x- intercepts

The vertex lies on the axis of symmetry which is situated at the midpoint of the x- intercepts

x- coordinate of vertex =
`(4+8)/(2)` = 6

f(6) = (6 - 8 )(6 - 4 ) = -2 × 2 = - 4 ← y-coordinate

vertex = (6, - 4 ) → B