How do you determine the values of a, b, and c from the equation $$4x^2 - 8x = 3$$ ?

Rearranging to standard form gives $$4x^2 - 8x - 3 = 0$$ . Thus, a = 4, b = -8, c = -3.

What does a negative discriminant indicate?

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Solve the equation using the quadratic formula: $$2x^2 - 5x + 1 = 0$$ .

Using the quadratic formula, the solutions are $$x = \frac{5 \pm \sqrt{17}}{4}$$ .

Solve the equation using the quadratic formula: $$0 = -2x^2 + 3x + 1$$ .

Rearranging gives $$2x^2 - 3x - 1 = 0$$ . The solutions are $$x = \frac{3 \pm \sqrt{17}}{4}$$ .

What is the vertex form of a quadratic equation?

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

How can you find the vertex of a quadratic equation in standard form?

The vertex can be found using the formula $$h = -\frac{b}{2a}$$ and then substituting h back into the equation to find k.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line given by $$x = -\frac{b}{2a}$$ , which divides the parabola into two mirror-image halves.

Identify the values of a, b, and c in the equation $$x^2 - 6x + 14$$ .

In the equation, a = 1, b = -6, c = 14.

What is the significance of the leading coefficient 'a' in a quadratic equation?

The leading coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

QUADRATIC FORMULA Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

Identify the standard form of a quadratic equation.

Back

3.

FLASHCARD QUESTION

Front

What do the coefficients a, b, and c represent in a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the discriminant in the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B

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