In this family, we have a slightly different quadratic function that shows us, very clearly, how the parabola shifts horizontally. P indicates the number of steps the parabola will move horizontally, to the right or to the left. If P is positive: (there is a minus sign in the equation) - The parabola will move P steps to the right. If P is negative: (and, consequently, there will be a plus sign in the equation since minus by minus equals plus) - The parabola will move P steps to the left.
Let's see an example: The function Y=(X+2)2
shifts two steps to the left. Let's see it in an illustration:
When there is an a before the parentheses, it indicates the slope of the parabola. The larger the a, the closer the parabola will be to its axis of symmetry. Steeper - with a smaller opening. The smaller the a, the farther the parabola will be from its axis of symmetry. Less steep - with a larger opening.
Let's see an example that shows the balance between the change in slope and horizontal shift: For example, in the function
the changes will be: Shift of 2 steps to the right and the change in slope, The parabola will be less steep and with a larger opening Let's see it in an illustration:
Graphical and Algebraic Solution wheny=0
when y=0 the expression inside parentheses must be equal to 0. X must be equal to P for the equation to be correct.
The graphical solution is the vertex of the parabola. In a quadratic function of this form Y=(X−p)2 in which the coefficient of X2 is 1, the vertex of the parabola is composed ofY=0 and byP which indicates the X vertex. (0,P) Note that, when in the equation there is a minus sign before theP indeed, it is positive and, when there is a plus sign before the P it is, in fact, negative.
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