SOLUTION: Find the vertex, the line of symmetry, the maximum or min value of the quadratic function. f(x)=4x^2-16x+19

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex, the line of symmetry, the maximum or min value of the quadratic function. f(x)=4x^2-16x+19      Log On


   

Question 323631: Find the vertex, the line of symmetry, the maximum or min value of the quadratic function.
f(x)=4x^2-16x+19
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert to vertex form, y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
f%28x%29=4x%5E2-16x%2B19
f%28x%29=4%28x%5E2-4x%29%2B19
f%28x%29=4%28x%5E2-4x%2B4%29%2B19-16
f%28x%29=4%28x-2%29%5E2%2B3
Comparing, the vertex is (2,3).
The vertex lies on the axis of symmetry x=2.
The parabola opens upwards since the coefficient of the x%5E2 term is positive so the vertex value is the minimum value.
ymin=3
.
.
.