Question

Y=x^2-8x+13 indentify the vertex and axis of symmetry

Answer 1

vertex = (4, - 3 ) and x = 4

Explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

y = x² - 8x + 13 ← is in standard form

with a = 1, b = - 8 , then

`x_(vertex)` = -
`(-8)/(2)` = 4

substitute x = 4 into y for corresponding y- coordinate

y = 4² - 8(4) + 13 = 16 - 32 + 13 = - 3

vertex = (4, - 3 )

the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex ) , then

equation of axis of symmetry is x = 4