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When k in the equation y=a(x-h)^2+k is negative, what happen? The parabola shifts DOWN (A part of your vertex). Example: y=x^2-7, the parabola will shift DOWN 7 units (vertex: (0,-7))
When k in the equation y=a(x-h)^2+k is positive, what happen? The parabola shift UP (A part of your vertex). Example: y=x^2+2, the parabola will shift UP 2 units (vertex: (0,2))
When h in the equation y=a(x-h)^2+k is negative, what happens? The parabola shifts RIGHT (A part of your vertex). Example: y=(x-3)^2, the parabola will shift RIGHT 3 units (vertex: (3,0)). Another way to remember: If it's in parenthesis, it will do the opposite.
When h in the equation y=a(x-h)^2+k is positive, what happens? The parabola shifts LEFT (A part of your vertex). Example: y=(x+4)^2, the parabola will shift LEFT 4 units (vertex: (-4,0)). Another way to remember: If it's in parenthesis, it will do the opposite.
What does the a in the equation y=a(x-h)^2+k do? This dictates whether the parabola will WIDEN or become more NARROW. Example: y=1/4x^2 will WIDEN y=5x^2 will become more NARROW
What will the equation: y=(x-3)^2+7 look like on a graph? A parabola shifted RIGHT 3 units and UP 7 units. Vertex: (3,7)
What will the equation: y=(x+2)^2-3 look like on a graph? A parabola shifted LEFT 2 units and DOWN 3 units. Vertex: (-2,-3)
What will the equation: y=1/3(x-4)^2+6 look like on a graph? A parabola shifted RIGHT 4 units, UP 6 units, and wider. Vertex: (4,6)
If given a quadratic equation in standard form (ax^2+bx+c), how can you find the vertex? The 'Vertex Formula': -b/2a will give you the x part of your vertex. Then plug in the x and solve for y.
What is the vertex for y=x^2+6x-7? -6/2(1)= -3 (-3)^2+6(-3)-7= -16 Therefore, your vertex is: (-3,-16)
How do you find the y-intercept? Replace x with 0 and solve for y. Example: y=(x-2)^2-1, y-intercept: (0,-1) y=x^2+4x-6, y-intercept: (0,-6) NOTE: THERE WILL ALWAYS BE A Y-INTERCEPT BUT NOT ALWAYS A X-INTERCEPT.
How do you know if a parabola faces upwards or downwards? Look at your y=a(x-h)^2+k, if a is a POSITIVE then it faces UPWARDS, if a is a NEGATIVE, then it faces DOWNWARDS.
Created by: careyann