a Consider the rule's constant and coefficient to the x-term.
B
b Consider the rule's constant and coefficient to the x-term.
C
c Consider the rule's constant and coefficient to the x-term.
A
a Graph 2
B
b Graph 3
C
c Graph 1
Practice makes perfect
a To identify the graph of a quadratic function, a good place to start is to look at the constant. This is because the constant tells us where the function intercepts the y-axis
y=- x^2 - 2
The y-intercept is y=- 2, which means we have two graphs to choose from, Graph 2 and Graph 3.
To determine which graph corresponds to Equation A we have to examine the coefficient of x^2. A negative coefficient makes the graph open downwards. Therefore, Equation A must correspond to Graph 2.
b From Part A we know that a function's constant shows where it intercepts the y-axis. We also know that a negative coefficient makes a parabola open downwards. Conversely, a positive coefficient makes the parabola open upwards. Therefore, Equation B must correspond to Graph 3.
c Examining the equation, we see that it has a constant of 2 and a negative x^2-term. This means it intercepts the y-axis at (0,2) and opens downwards. Therefore, Equation C must correspond to Graph 1.
