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 $$x^2 - 8x + 16 = (x - 4)^2$$ .

How do you complete the square for the equation $$x^2 - 8x$$ ?

To complete the square, take half of the coefficient of $$x$$ (which is -8), square it (resulting in 16), and add it to both sides: $$x^2 - 8x + 16 = 16$$ .

What is the axis of symmetry in a quadratic function?

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

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

The vertex represents the maximum or minimum value of the quadratic function, depending on the direction the parabola opens.

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

The sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

What does it mean for a quadratic equation to have no real solutions?

A quadratic equation has no real solutions when the discriminant is negative (i.e., $$b^2 - 4ac

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

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

How can you determine the number of real solutions from a graph of a quadratic function?

You can determine the number of real solutions by observing the number of times the graph intersects the x-axis: two intersections mean two real solutions, one intersection means one real solution, and no intersections mean no real solutions.

Solving Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does the graph of a quadratic equation look like?

Back

4.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens downwards or upwards.

5.

FLASHCARD QUESTION

Front

How do you find the roots of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

7.

FLASHCARD QUESTION

Front

What does the discriminant tell us about a quadratic equation?

Back

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