Solve the equation $$x^2 = 52$$ .

x = $$2\\sqrt{13}, -2\\sqrt{13}$$ .

What is the formula for the vertex of a parabola given by $$y = ax^2 + bx + c$$ ?

Vertex: $$(-\frac{b}{2a}, f(-\frac{b}{2a}))$$ .

What is the discriminant in the quadratic formula and what does it indicate?

Discriminant: $$D = b^2 - 4ac$$ ; indicates the nature of the roots (real and distinct, real and equal, or complex).

What is the quadratic formula?

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is a rational solution in the context of quadratic equations?

A solution that can be expressed as a fraction of two integers.

What is the significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola.

How do you find the x-intercepts of a quadratic equation?

Set $$y = 0$$ and solve for $$x$$ using factoring, completing the square, or the quadratic formula.

What is the axis of symmetry in a quadratic function?

The vertical line that divides the parabola into two mirror images, given by $$x = -\frac{b}{2a}$$ .

What does it mean for a quadratic equation to have complex solutions?

It means the solutions involve imaginary numbers, occurring when the discriminant is negative.

MTH 610 Core Final Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

Left 2

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

(-4, -5)

4.

FLASHCARD QUESTION

Front

How many and what type of solutions does the equation 3m^2 - 6m + 3 = 0 have?

Back

1 rational

5.

FLASHCARD QUESTION

Front

Solve using the quadratic formula: 2x^2 - 9x - 35 = 0.

Back

6.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

Back

The direction of the parabola (upward if a > 0, downward if a < 0).

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