How do you find the axis of symmetry for a parabola?

The axis of symmetry for a parabola given by the equation $$y = ax^2 + bx + c$$ is the vertical line $$x = -\frac{b}{2a}$$ .

What is the quadratic formula?

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

What does the discriminant of a quadratic equation tell us?

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

How do you convert a quadratic equation from vertex form to standard form?

To convert from vertex form $$y = a(x - h)^2 + k$$ to standard form, expand the equation: $$y = a(x^2 - 2hx + h^2) + k$$ .

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 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 do you determine if a quadratic function opens upwards or downwards?

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

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

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

Understanding Quadratics Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does the vertex of a parabola represent?

Back

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

3.

FLASHCARD QUESTION

Front

How do you convert a quadratic equation from intercept form to standard form?

Back

4.

FLASHCARD QUESTION

Front

What are the x-intercepts of a quadratic function?

Back

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