A parabola has a vertex at (5,4) and passes through (6,134). What are the x-intercepts?
1 Answer
Mar 2, 2017
The x-intercepts are given by
Explanation:
Start by finding the equation of the parabola. The vertex form of a parabola, with vertex
y=a(x−p)2+q
We know an x-value, a y-value and the vertex. We can therefore set up an equation and solve for
134=a(6−5)2+4
134=a(1)2+4
−34=a
The equation is therefore
y=−34(x−5)2+4
We can solve for the x-intercepts by taking the square root. Set
0=−34(x−5)2+4
−4=−34(x−5)2
−4−34=(x−5)2
163=(x−5)2
±4√3=x−5
x=5±4√3
x=5±4√33
A graphical depiction of the parabola confirms our findings.
graph{y = -3/4(x - 5)^2 + 4 [-10, 10, -5, 5]}
Hopefully this helps!
