What does the coefficient $$a$$ in a quadratic equation determine?

The coefficient $$a$$ determines the direction of the parabola's opening. If $$a > 0$$ , the parabola opens upwards; if $$a

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of a quadratic equation.

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

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 do you determine the direction a parabola opens?

The direction a parabola opens is determined by the sign of the coefficient $$a$$ in the quadratic equation: positive opens upwards, negative opens downwards.

What is the maximum height of a projectile modeled by a quadratic function?

The maximum height can be found by determining the vertex of the quadratic function that models the projectile's height.

What is the formula for the height of a projectile thrown upwards?

The height of a projectile can be modeled by the equation $$h(t) = -16t^2 + vt + h_0$$ , where $$v$$ is the initial velocity and $$h_0$$ is the initial height.

What does the term 'vertex' refer to in the context of parabolas?

In the context of parabolas, the vertex refers to the point where the parabola changes direction, representing either the maximum or minimum value of the function.

How can you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve through them.

Parabolas & Quadratics Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that is defined by a quadratic function. It can open upwards or downwards depending on the coefficient of the squared term.

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a parabola?

Back

6.

FLASHCARD QUESTION

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. You can find it by substituting the x-coordinate of the vertex back into the function.

7.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

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