Video Transcript
Which of the following graphs
represents the quadratic function 𝑦 equals 𝑥 squared minus four?
We begin by examining the five
graphs provided on the 𝑥𝑦-coordinate plane, and we notice that all five graphs
have symmetry in the 𝑦-axis. We recall that quadratic graphs of
the form 𝑓 of 𝑥 equals 𝑘𝑥 squared plus 𝑐 are symmetric parabolas with a line of
symmetry 𝑥 equals zero, or the 𝑦-axis. The 𝑦-intercept for the graph of
𝑓 of 𝑥 equals 𝑘𝑥 squared plus 𝑐 is the coordinate point zero, 𝑐.
We also recall that a positive
𝑘-value results in a parabola that resembles a u shape and a negative 𝑘-value
results in a parabola that resembles an n shape. This will help us distinguish
between the five graphs given in the diagram. We notice that the function we have
been given is of the form 𝑓 of 𝑥 equals 𝑘𝑥 squared plus 𝑐, where 𝑘 equals one
and 𝑐 equals negative four. This means the graph we are looking
for has a 𝑦-intercept at the point zero, negative four.
We notice that both the purple
graph C and the green graph E have the desired 𝑦-intercept. So, we can eliminate the other
options with 𝑦-intercepts at zero, zero or zero, four. We will now look for the
differences between the remaining graphs of C and E. And we notice that C opens upward
in a u shape and E opens downward in an n shape. Since our 𝑘-value of one is
positive, we expect a parabola that opens upward. So, we eliminate option E because
that parabola opens downward.
Therefore, it is graph C that
represents the quadratic function 𝑦 equals 𝑥 squared minus four.
