What is the decreasing interval of the quadratic function $$f(x) = x^2 - 2x + 3$$ ?

The decreasing interval is $$(-\text{∞}, 1)$$ .

What is the vertex of the quadratic function $$f(x) = 2x^2 - 8x + 6$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ . Here, the vertex is at (2, -6).

What is the axis of symmetry for the quadratic function $$f(x) = x^2 + 4x + 4$$ ?

The axis of symmetry is the line $$x = -2$$ .

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

A quadratic function opens upwards if the coefficient of $$x^2$$ is positive and downwards if it is negative.

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

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

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

What are the key features of the graph of a quadratic function?

Key features include the vertex, axis of symmetry, x-intercepts, y-intercept, and whether it opens upwards or downwards.

How do you find the y-intercept of a quadratic function?

The y-intercept can be found by evaluating the function at $$x = 0$$ .

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex.

What is the effect of changing the value of 'a' in the quadratic function $$f(x) = ax^2$$ ?

Changing the value of 'a' affects the width and direction of the parabola: larger |a| makes it narrower, while smaller |a| makes it wider.

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

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

Characteristics of Quadratic Functions

Flashcard

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Mathematics

•

9th Grade

•

Practice Problem

•

Medium

•

CCSS

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

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FLASHCARD QUESTION

Front

What is the parent function of quadratic functions?

Back

FLASHCARD QUESTION

Front

How do you find the x-intercepts of a quadratic function?

Back

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