Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the formula used to graph a parabola in standard form?

1. y = ax² + bx + c

2. y = a(x - h)² + k

3. y = mx + b

4. y = ax + b

The correct answer is: y = ax² + bx + c

The formula used to graph a parabola in standard form is represented by the equation \( y = ax^2 + bx + c \). This is known as the quadratic equation, which is the standard form for any quadratic function. In this equation, the coefficient \( a \) determines the direction and the width of the parabola. If \( a \) is positive, the parabola opens upwards, and if \( a \) is negative, it opens downwards. The coefficients \( b \) and \( c \) contribute to the position of the parabola along the x-axis and the y-axis, respectively. This form is particularly useful for identifying the vertex and the axis of symmetry of the parabola, although additional steps may be needed to convert to vertex form, which is represented in another option. The other formulas provided correspond to different types of functions: one represents the vertex form of a parabola, another describes a linear relationship, and the last also illustrates a linear function. Each serves different purposes in graphing and analyzing mathematical relationships.