




Understand that the x-intercepts of a quadratic
relation are the solutions to the quadratic
equation
Factor a quadratic relation and find its xintercepts, and then sketch the graph
Solve real-world problems by factoring a
quadratic equation and finding the intercepts of
the corresponding quadratic relation
Determine the equation of a quadratic relation in
the form y = a(x – r)(x – s) from a graph
y  x  2x  8
2

Set y = 0 and solve for x:
x  2x  8  0
2
vertex  (1,9)
y
( x  4)(x  2)  0






x  4  0, x  2  0



x







x  4, x  2














The x-intercepts(or zeros) of the quadratic
relation
2
y  ax  bx  c

are the solutions to the quadratic equation
ax  bx  c  0
2

If the x-intercepts r and s are found, the xcoordinate of the vertex is
rs
2

The y-coordinate of the vertex is found by
substituting the x-coordinate into the original
equation.
y  2x  x  6
2

SOLUTION:
y









x




















y  x  4x  4
2

SOLUTION:
y









x












y  x  3x  4
2

SOLUTION:
y









x















1) Two x-intercepts – two different factors
leads to two solutions – graph crosses twice.
2) One x-intercept – factor is a perfect square
that leads to one solution – graph just
touches the x-axis.
3) No x-intercepts – cannot solve the
quadratic equation by factoring – graph never
touches the x-axis.
y






















x













An engineer uses the equation
h  d 2  25
to design an arch, where h is the height in
metres and d is the horizontal distance in
metres.
How wide and tall is the arch?


Solution:
y














x













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6.3 Graphing a Quadratic Equation by Factoring First