How do you graph #f(x)=-x^2+2x+5# and identify the x intercepts, vertex?
1 Answer
You can find the roots using the quadratic equation and the vertex using the formula
Explanation:
Recall the general form of a quadratic function:
VERTEX: The vertex has an
Y-INTERCEPT: The graph crosses the
X-INTERCEPT: To find the
Substituting gives us
as our roots, or
Alternatively, we could try factorising the quadratic manually, this is easier if the quadratic has integer roots (or rational roots). In this case, we can't (well, we can, but not in terms of rational numbers).
Together, the roots, the vertex, and the
Also, since the leading coefficient is negative, you know that the quadratic must but an upside-down U.