Unit 2 – NonLinear Equations
Lesson 2 – Quadratic Graphs and Equations
SlowMotion Tennis Ted White
This picture was produced in a dark
room, with a strobe light and a camera
that was capable of taking long exposure
shots (by keeping its shutter open longer).
The parabolic shapes brilliantly
demonstrate the relative time that it takes
for the ball to travel throughout the various
points of the image. At the very top of
the parabola, the tennis ball images appear
very close together, therefore indicating
that the ball moved at a slower velocity.
Conversely, near the bottom of the
parabolas, the distances between the
images of the ball grow larger, therefore
indicating that the ball moved more space
per time interval as it descended toward
the racket. This slowmotion tennis
picture helps one more easily visualize the
properties of parabolic motion, as defined
by Earth's gravitational force.
The equation of a quadratic function is
y = ax2 + bx + c y=ax2 + bx + c
The shape of this function’s graph is a parabola.
Some parabolas have a minimum and some have a
• If a is positive, the parabola opens upward, and the
parabola has a minimum.
• If a is negative, the parabola opens downward, and the
parabola has a maximum.
The zeros of a quadratic function are the xcoordinates where the
function intercepts the xaxis.
They are found when y=0. Parabolas may have 0, 1 or 2 zeros.
0 xintercepts 1 xintercept 2 xintercepts
The vertex is the maximum/minimum point of the parabola.
The vertex is the place where the parabola changes direction.
The vertex is identified by x and ycoordinates
If the vertex is identified by x and ycoordinates
e.g. (1.5,1), then..
The axis of symmetry is the vertical line through the vertex. Its equation is x = m where m is the x
value of the vertex.