Question

The graph y = 1/2x^2 - x - 4 is shown below. State the coordinate of the zero(s):

Answer 1

Zeros → (-2, 0) and (4, 0)

Explanation:

Equation of the graph has been given as,

y =
`(1)/(2)x^(2) -x-4`

For zeros of the function,

y = 0

Therefore,
`(1)/(2)x^(2) -x-4=0`

By solving the equation algebraically,

x² - 2x - 8 = 0

x² - 4x + 2x - 8 = 0

x(x - 4) + 2(x - 4) = 0

(x + 2)(x - 4) = 0

x = -2, 4

Therefore, coordinates of the zeros will be (-2, 0) and (4, 0).

Let's confirm the zeros (x-intercepts) from the graph attached,

Coordinates of the x-intercepts are,

(-2, 0) and (4, 0)