For the quadratic function $$y = ax^2 + bx + c$$ , what is the general shape of its graph?

The graph of a quadratic function is a parabola, which opens upwards if $$a > 0$$ and downwards if $$a

What is the vertex of the quadratic function $$y = 2x^2 - 4x + 1$$ ?

The vertex can be found using $$x = -\frac{-4}{2(2)} = 1$$ . Substituting back, $$y = 2(1)^2 - 4(1) + 1 = -1$$ . So, the vertex is (1, -1).

What is the effect of changing the value of 'a' in the quadratic function $$y = ax^2$$ ?

Changing 'a' affects the width and direction of the parabola. If $$|a| > 1$$ , the parabola is narrower; if $$0

What is the domain of the quadratic function $$y = x^2 - 3x + 2$$ ?

The domain of any quadratic function is all real numbers, or in interval notation: $$(-\infty, \infty)$$ .

What is the range of the quadratic function $$y = -x^2 + 4$$ ?

The range is all values less than or equal to 4, or in interval notation: $$(-\infty, 4]$$ .

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

The y-intercept of a quadratic function $$y = ax^2 + bx + c$$ is found by evaluating the function at $$x = 0$$ , which gives $$y = c$$ .

What is the y-intercept of the function $$y = 3x^2 + 2x - 5$$ ?

The y-intercept is $$y = -5$$ , which occurs at the point (0, -5).

What does it mean for a quadratic function to be increasing or decreasing?

A quadratic function is increasing on the interval where the slope is positive (to the right of the vertex) and decreasing where the slope is negative (to the left of the vertex).

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 distinct real roots; if $$D = 0$$ , there is one real root; if $$D

How do you express the range of a quadratic function in vertex form?

In vertex form $$y = a(x - h)^2 + k$$ , the range is determined by the vertex (h, k). If $$a > 0$$ , the range is $$[k, \infty)$$ ; if $$a

domain and range quadratics Flashcards

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FLASHCARD QUESTION

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What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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