Identify the vertex and the axis of symmetry for the graph of y=5(x-2)^2 + 3.

Question

a) vertex (2,3); x = -2
b) vertex (-2,-3); x = 2
c) vertex (2,3); x = 2
d) vertex (-2,-3); x = -2

I have no idea how to solve this problem! Please help. Thank you! :)

Answer 1

All parabolas of the form
y=ax² + bx + c
have their axis of symmetry passing through the vertex.

Thus a and b can be eliminated on that basis.

Note that when the x² term is positive, the parabola has a minimum at the vertex.

By inspection, when x=2, the value of y is at its minimum because the 5(x-2)² term is zero. Any other value of x will render the term > 0. Thus the vertex is at x=2, where y=3.
Thus the answer is (C).

Check:
c. y=5(2-2)²+3=3
d. y=5(-2-2)²+3=83 (not equal to 3)