Answer:
f(x) = x² + 2x - 3 ..….equation1
The graph of function will be a parabola
Standard form of parabola:
y=ax²+bx+c
x-coordinate of the vertex can be found using
x = [tex]\frac{−b}{2a}[/tex]
from equation 1 find values for a, b, and c.
a = 1, b = 2, c = -3 ⇒ x=−2/2(1) ⇒ x = -1
substitute the value of x into equation 1 for y-coordinate
f(-1) = (-1)² + 2(-1) – 3 ⇒ −4
vertex =(-1,−4)
Axis of symmetry = x = -1,
Axis of symmetry is vertical and passes through the vertex with equation
x = -1
For x-intercept, put y = 0
x² + 2x - 3=0 ⇒ x² + 3x -x - 3=0 ⇒ x( x + 3 ) -1 ( x + 3 ) ⇒ ( x − 1 )( x + 3 ) = 0
equate each factor to zero and solve for x
x − 1 = 0 ⇒ x = 1, x + 3 = 0 ⇒ x = -3
x-intercept = { 1, -3 }
For y-intercepts put x = 0
y = (0)² + 2(x) - 3
y = -3
y-intercept = ( 0 , -3 )
The points for the vertex, x-intercepts, and y-intercept and axis of symmetry are plotted on the graph.
