Graph each function. Calculate the vertex (both x and y). Please include a table of values.

Question

Answer 1

x^2 -4x + 1 complete the square, add and subtract 4

x^2 -4x + 4 +1 -4

(x^2 -2)^2 -3 vertex is (2,-3) general form is (x-h)^2 + k where (h,k) is the vertex

it's an upward opening parabola

y intercept (0,1) axis of symmetry x=2, so (4,1) is also a point on the parabola

-2x^2 -8x -3 divide by -2

x^2 +4x +3/2 complete the square add and subtract 4

x^2 +4x +4 + 3/2 -4

(x+2)^2 - 5/2 vertex is (-2,-5/2)

It's a downward opening parabola. y intercept = (0,-3) axis of symmetry: x=-2, so another point on the parabola is (-4,-3)

draw a smooth parabolic curve through the 3 points