What does it mean for a quadratic equation to be in standard form?

A quadratic equation is in standard form when it is expressed as $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

What is the vertex form of a quadratic equation?

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

How can you determine if a quadratic opens upwards or downwards?

A quadratic opens upwards if the coefficient a > 0 and downwards if a

What is the significance of the y-intercept in a quadratic equation?

The y-intercept of a quadratic equation is the point where the graph intersects the y-axis, found by evaluating the equation at x = 0, which gives $$c$$ .

What is completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to solve for x.

How do you solve a quadratic equation by factoring?

To solve a quadratic equation by factoring, set the equation to zero, factor it into two binomials, and then set each binomial equal to zero to find the roots.

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

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

What is the role of the constant term in a quadratic equation?

The constant term (c) in a quadratic equation affects the position of the parabola on the y-axis and determines the y-intercept.

Quadratic Equations and Their Solutions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

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What are the zeros of a quadratic equation?

Back

The zeros (or roots) of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

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