What does the discriminant tell you about a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if

What are the x-intercepts of a quadratic function?

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by solving $$y = 0$$ .

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 images, given by $$x = -\frac{b}{2a}$$ .

How do you determine the direction of a parabola?

The direction of a parabola opens upwards if $$a > 0$$ and downwards if $$a

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

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and is found using the vertex form or by completing the square.

How do you write a quadratic equation given its roots?

If the roots are r_1 and r_2, the quadratic equation can be written as $$y = a(x - r_1)(x - r_2)$$ .

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

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

How can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw the parabola.

Writing Quadratic Equations

Flashcard

•

Mathematics

•

8th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSF-IF.C.7A, HSA-SSE.B.3B

Standards-aligned

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FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

FLASHCARD QUESTION

Front

What is factored form of a quadratic equation?

Back

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