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

Mar 18, 2016

vertex (1, 4)

#### Explanation:

x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{2}{-} 2 = 1$
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
$- {x}^{2} + 2 x + 3 = 0$
Since (a - b + c = 0), use shortcut. The 2 real roots (x -intercepts) are:
- 1 and $\left(- \frac{c}{a} = 3\right)$