Question

The graph of which of the following functions has a vertex at (4, -3)?

f(x) = x2² + 8x + 19
f(x) = x² - 8x + 19
f(x) = x² + 8x + 13
f(x) = x² - 8x + 13

Answer 1

Therefore the answer is the fourth option y = f(x) =
`x^(2)` - 8x + 13

Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.

Explanation:

i) f(x) =
`x^(2)` + 8x + 19 =
`(x + 4)^(2)` + 3. SO the vertex is at (-4, 3)

Therefore the answer is the fourth option y = f(x) =
`x^(2)` - 8x + 13

= (
`x^(2)` - 8x + 16) + 3 =
`(x-4)^(2)` - 3

Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.