Sem 1 Review Part 1

Front

What is exponential growth?

Back

Exponential growth refers to an increase that occurs at a rate proportional to the current value, resulting in a rapid increase over time. It is often represented by the equation f(x) = a * b^x, where b > 1.

Front

What is the vertex of a parabola in the form y = a(x - h)^2 + k?

Back

The vertex of a parabola in this form is the point (h, k). It represents the highest or lowest point of the parabola depending on the value of 'a'.

Front

How do you find the vertex of the parabola given by the equation y = 3(x + 5)^2 - 4?

Back

To find the vertex, identify h and k from the equation in vertex form y = a(x - h)^2 + k. Here, h = -5 and k = -4, so the vertex is (-5, -4).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of f(x) = (x - 1)^2 - 5 represent?

Back

This graph represents a parabola that opens upwards with its vertex at the point (1, -5).

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises sharply to the right and approaches the x-axis but never touches it, indicating that it is asymptotic to the x-axis.

Front

How can you identify exponential growth from a sequence of numbers?

Back

Exponential growth can be identified in a sequence of numbers if each term is a constant multiple of the previous term, such as 2, 4, 8, 16, 32, 64.

Front

What is the equation of a parabola that opens downwards?

Back

The equation of a parabola that opens downwards can be written in vertex form as y = -a(x - h)^2 + k, where a > 0.

Front

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

Back

The coefficients of a quadratic equation (a, b, c) affect the width, direction, and position of the parabola on the graph. The sign of 'a' determines if it opens upwards or downwards.