Quadratic Functions and Graphs
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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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))
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| 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))
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| 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.
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| 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.
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| 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
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| 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)
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| 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)
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| 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)
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| 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.
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| 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)
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| 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.
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| 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.
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To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
careyann
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