Question

Find the vertex and all intercepts of the parabola. Then sketch and determine window values. The problem is: f(x)=-x^2-2x+3

Answer 1

the formula to find the mim/max point of a parabola is
\[x=-\frac{b}{2a}\]
so
\[x = \frac{2}{-2} = -1\]
so y = 4
so the vertex is (-1, 4)

to find the intercepts just set x and y equal to 0 one by one
the equation is
y = -x^2 - 2x + 3
y = 0
0 = -x^2 - 2x + 3
x^2 + 2x -3 = 0
(x - 1)(x + 3) = 0
x = 1, -3
so the x intercepts are (1, 0) and (-3, 0)

x = 0
y = 3
y intercept is (0, 3)