How do you find the value to complete the square for $$x^2 - 14x + ____$$ ?

Take half of the coefficient of $$x$$ (which is -14), square it, resulting in 49.

How do you solve the equation $$x^2 = 9 - 4x$$ by completing the square?

Move -4x to the left side to get $$x^2 + 4x = 9$$ , then complete the square.

What is the solution to the equation $$3x^2 + 15 = 18x$$ after completing the square?

The solutions are $$x = -1$$ and $$x = 5$$ .

What is the significance of the discriminant in completing the square?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation.

What does it mean if the discriminant is zero?

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How can completing the square help graph a quadratic function?

It allows you to find the vertex and axis of symmetry, making it easier to sketch the graph.

What is the relationship between the coefficients and the vertex in the standard form of a quadratic?

The vertex can be found using the formula $$(-\frac{b}{2a}, f(-\frac{b}{2a}))$$ .

Completing the square Flashcards

Student preview

15 questions

Show all answers

1.

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, allowing for easier solutions.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

Subtract 21 from both sides to isolate the quadratic and linear terms.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What do you do to the b value to correctly complete the square?

Back

Divide it by 2 and square the result.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the formula for completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

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