Question

. Algebra 2Parabolas--Homeworkidentify the vertex and axis of symmetry of each. Then sketch the graph.

Answer 1

Rewrite the given function into vertex form :

`y=-x^2+10x-25`

Factor out the coefficient of x^2

`y=-(x^2-10x+25)`

Note that the trinomial inside the parenthesis is a perfect square, this will be :

`y=-(x-5)^2`

The vertex of a parabola in the form y = a(x - h)^2 + k is (h, k) and the axis of symmetry is

x = h

From the equation we have, the vertex will be at (5, 0) and the axis of symmetry is x = 5

Note that the parabola opens downward if the sign of x^2 is negative.

The graph will be :