How do you find the important points to graph y = -x^2 + 3?

1 Answer
Jul 2, 2018

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

Explanation:

Given: y = -x^2 + 3

With the equation in the form: Ax^2 + Bx + C = 0,

the vertex is at (-B/(2A), f(-B/(2A))),

the axis of symmetry is x = -B/(2A)

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

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

For the given equation:

-B/(2A) = 0/-2 = 0

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

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

color(blue) ("Find x-intercepts") by setting y = 0:

0 = -x^2 + 3

-3 = -x^2

x^2 = 3 => x = +- sqrt(3)

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

color(red) ("Find y-intercept") by setting x = 0:

y = -(0)^2 + 3 => y = 3

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