Question

A parobola has the equation y=x²+2x-3

What are the coordinates of the turning point of the parabola? what is the equation of the axis of symmetry for this parabola?​

Answer 1

(- 1, - 4 ) and x = - 1

Explanation:

given a parabola in standard form

y = ax² + bx + c ( ax≠ 0 )

then the x- coordinate of the vertex is

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

y = x² + 2x - 3 ← is in standard form

with a = 1, b = 2 , then

x = -
`(2)/(2)` = - 1

substitute x = - 1 into the equation for corresponding y- coordinate

y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4

vertex = (- 1, - 4 )

this is an upward opening parabola ( a > 0 )

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 is

x = - 1

Answer 2

(-1,-4) is the vertex

x = -1 is the equation of symmetry;

Explanation:

See attached image.