What does the discriminant tell us about a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

How do you factor a quadratic equation?

To factor a quadratic equation of the form $$ax^2 + bx + c$$ , find two numbers that multiply to $$ac$$ and add to $$b$$ .

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.

What is the y-intercept of a quadratic function?

The y-intercept of a quadratic function is the point where the graph crosses the y-axis, found by evaluating the function at $$x = 0$$ .

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

The leading coefficient $$a$$ determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

How can you determine if a quadratic equation can be factored?

A quadratic equation can be factored if its discriminant is a perfect square, indicating that the roots are rational.

What is the relationship between the roots and the coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is a perfect square trinomial?

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as $$(x + a)^2 = x^2 + 2ax + a^2$$ .

Solving Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

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2.

FLASHCARD QUESTION

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What is the standard form of a quadratic equation?

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3.

FLASHCARD QUESTION

Front

What does the graph of a quadratic equation look like?

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