*Name the 4 different types of shifts that are possible with a quadratic equation.*

How is it expressed in the equation?

if a quadratic equation is graphed with a shift upward, how is that expressed in its equation? It is shown as x^2 + x, or x^2 + 1, or x^2 – x, or x^2 – 1.

The shifts of a quadratic equation are expressed in each equation through a formula. Please provide those formulas with a corresponding brief description of what does that equation represent. For example, if you provide a formula for a quadratic equation that shifts upward, then give the formula and then state it is a quadratic equation that shifts upward.

Another example, if you have

• f(x) = x2 + 1 upward 6 units.

Then its answer is (x^2 +1) + 6 simplified to x^2 + 7.

Or

If you have

• f(x) = (x + 6)2 to the right 10 units.

How is this shown in an equation? (if you know the formula, you will know how to do it that way as well?

How is it expressed in the equation?

if a quadratic equation is graphed with a shift upward, how is that expressed in its equation? It is shown as x^2 + x, or x^2 + 1, or x^2 – x, or x^2 – 1.

The shifts of a quadratic equation are expressed in each equation through a formula. Please provide those formulas with a corresponding brief description of what does that equation represent. For example, if you provide a formula for a quadratic equation that shifts upward, then give the formula and then state it is a quadratic equation that shifts upward.

Another example, if you have

• f(x) = x2 + 1 upward 6 units.

Then its answer is (x^2 +1) + 6 simplified to x^2 + 7.

Or

If you have

• f(x) = (x + 6)2 to the right 10 units.

How is this shown in an equation? (if you know the formula, you will know how to do it that way as well?

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