SOLUTION: I need help find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. I'm completely stumped on this topic. The formula is y=ax^2+bx+c Question: y=x^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I need help find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. I'm completely stumped on this topic. The formula is y=ax^2+bx+c Question: y=x^2      Log On


   

Question 698279: I need help find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. I'm completely stumped on this topic. The formula is y=ax^2+bx+c Question: y=x^2+2x+1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc+
Question: y=x%5E2%2B2x%2B1
To find the vertex of a parabola, we will write the function in the form y=a%28x-h%29%5E2%2Bk+ where (h,k) are the coordinates of vertex

y=%28x%2B1%29%5E2...=> h=-1, k=0; so, vertex is at (-1,0)
since a=1, parabola opens upward and has a minimum at x=-1
an axis of symmetry is the line that runs down its 'center or vertex' and this line divides the graph into two perfect halves; so in your case that line is vertical line that goes through x=-1

range: all non-negative real numbers y%3E=0