How do you determine the direction of a parabola from its equation?

The direction of a parabola can be determined by the sign of the coefficient 'a' in the standard form $$y = ax^2 + bx + c$$ . If 'a' is positive, it opens upwards; if negative, it opens downwards.

What is the axis of symmetry in a quadratic function?

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex, given by the equation $$x = h$$ , where (h, k) is the vertex.

How can you find the X-intercepts of a quadratic equation?

To find the X-intercepts, set the quadratic equation equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

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 is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ . It determines the nature of the roots.

What does the discriminant tell us about the roots of a quadratic equation?

If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if negative, there are no real roots.

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

The coefficient 'a' determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower.

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

To convert from standard form to vertex form, complete the square on the quadratic expression.

Quadratic Features Flashcards

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FLASHCARD QUESTION

Front

What are the X-intercepts of a quadratic function?

Back

The X-intercepts are the points where the graph of the quadratic function crosses the X-axis, represented as (x, 0).

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