SOLUTION: Graph the quadratic function {{{ f(x)=-x^2+2x+15 }}}; state the ordered pairs representing the x-intercept(s), y-intercept (if any), and the vertex of the parabola.

Algebra ->  Exponents -> SOLUTION: Graph the quadratic function {{{ f(x)=-x^2+2x+15 }}}; state the ordered pairs representing the x-intercept(s), y-intercept (if any), and the vertex of the parabola.      Log On


   

Question 367505: Graph the quadratic function +f%28x%29=-x%5E2%2B2x%2B15+; state the ordered pairs representing the x-intercept(s), y-intercept (if any), and the vertex of the parabola.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=-x%5E2%2B2x%2B15+
To find the y-intercept set x=0 and solve for f(x):
+f%280%29=-0%5E2%2B2%280%29%2B15+
+f%280%29=0%2B0%2B15+
+f%280%29=15+
y-intercept is at (0, 15)
.
To find the x-intercept set f(x)=0 and solve for x:
+0=-x%5E2%2B2x%2B15+
+0=x%5E2-2x-15+
+0=%28x-5%29%28x%2B3%29+
x = {-3, 5}
x-intercepts are at (-3,0) and (5,0)
.
Vertex:
x-coordinate:
x = -b/(2a) = -(2)/(2*(-1)) = -2/(-2) = 1
y-coordinate:
+f%281%29=-1%5E2%2B2%281%29%2B15+
+f%281%29=-1%2B2%2B15+
+f%281%29=1%2B15+
+f%281%29=16+
vertex is at (1, 16)