Question

How do you find the vertex and intercepts for `y=-x^2+2x+3`?

Answer 1

vertex (1, 4)

Explanation:

x-coordinate of vertex:
`x = -b/(2a) = -2/-2 = 1`
y-coordinate of vertex:
y(1) = -1 + 2 + 3 = 4
Vertex (1, 4)
To find y-intercept, make x = 0 --> y = 3
To find x-intercepts, make y = 0, and solve the quadratic equation
`-x^2 + 2x + 3 = 0`
Since (a - b + c = 0), use shortcut. The 2 real roots (x -intercepts) are:
- 1 and `(-c/a = 3)`