How do you find the important points to graph y=x2+3?

1 Answer
Jul 2, 2018

vertex (0,3)
x-intercepts: (3,0),(3,0)
y-intercept: (0,3)

Explanation:

Given: y=x2+3

With the equation in the form: Ax2+Bx+C=0,

the vertex is at (B2A,f(B2A)),

the axis of symmetry is x=B2A

If the coefficient A<0, the vertex is a maximum

If the coefficient A>0, the vertex is a minimum

For the given equation:

B2A=02=0

f(0)=(0)2+3=3

vertex (0,3) is a maximum; axis of symmetry: x=0

Find x-intercepts by setting y=0:

0=x2+3

3=x2

x2=3x=±3

x-intercepts: (3,0),(3,0)

Find y-intercept by setting x=0:

y=(0)2+3y=3

y-intercept: (0,3), which is the vertex