How do you complete the square for the equation $$p^2 + 2p - 63 = 0$$ ?

1. Move the constant to the other side: $$p^2 + 2p = 63$$ . 2. Take half of the coefficient of $$p$$ (which is 1), square it (1), and add it to both sides: $$p^2 + 2p + 1 = 64$$ . 3. Factor: $$(p + 1)^2 = 64$$ . 4. Solve: $$p + 1 = \text{±}8$$ , giving $$p = 7, -9$$ .

What value of 'c' completes the square for $$b^2 - 12b + c$$ ?

To complete the square, take half of -12 (which is -6), square it (36), so $$c = 36$$ . The expression becomes $$(b - 6)^2$$ .

How do you solve $$m^2 + 2m - 48 = -6$$ by completing the square?

1. Rearrange: $$m^2 + 2m = 42$$ . 2. Add 1 to both sides: $$m^2 + 2m + 1 = 43$$ . 3. Factor: $$(m + 1)^2 = 43$$ . 4. Solve: $$m + 1 = \text{±}\sqrt{43}$$ , giving approximate values of $$m = 5.55, -7.55$$ .

What is the significance of the term $$b/2$$ in completing the square?

The term $$b/2$$ is crucial because it helps to form the perfect square trinomial, allowing for easier factoring and solving of the quadratic equation.

How do you rewrite $$p^2 + 14p + c$$ as a perfect square?

To complete the square, take half of 14 (which is 7), square it (49), so $$c = 49$$ . The expression becomes $$(p + 7)^2$$ .

What is the solution to the equation $$x^2 + 6x + 9 = 0$$ using completing the square?

1. Recognize that $$x^2 + 6x + 9 = (x + 3)^2$$ . 2. Set $$(x + 3)^2 = 0$$ . 3. Solve: $$x + 3 = 0$$ , giving $$x = -3$$ .

What is the relationship between completing the square and the quadratic formula?

Completing the square is a method to derive the quadratic formula. It transforms the standard form of a quadratic equation into a solvable format.

How do you find the vertex of a parabola from the equation $$y = ax^2 + bx + c$$ using completing the square?

Rewrite the equation in vertex form by completing the square. The vertex is given by the point $$(-\frac{b}{2a}, f(-\frac{b}{2a}))$$ .

What is the first step in completing the square for any quadratic equation?

The first step is to ensure the coefficient of $$x^2$$ is 1. If it is not, divide the entire equation by that coefficient.

What does it mean if a quadratic equation has no real solutions when completing the square?

If, after completing the square, the expression results in a negative number set equal to zero (e.g., $$(x + p)^2 = -k$$ where $$k > 0$$ ), it indicates that there are no real solutions.

How can completing the square help in graphing quadratic functions?

Completing the square allows you to rewrite the quadratic function in vertex form, making it easier to identify the vertex and the direction of the parabola.

What is the value of 'c' that completes the square for $$m^2 + 4m + c$$ ?

To complete the square, take half of 4 (which is 2), square it (4), so $$c = 4$$ . The expression becomes $$(m + 2)^2$$ .

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Math

Algebra

Completing The Square

Completing the Square

Flashcard

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSA.APR.C.4, HSF-IF.C.7A

Standards-aligned

Wayground Content

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FLASHCARD QUESTION

Front

What is 'completing the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, which makes it easier to solve for the variable.

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is the formula for completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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