Aim #60: How do we graph quadratics with irrational roots?
Do Now: Find the roots of y = x2 - 4x + 1
For each function, identify the vertex, y-intercept, and x-intercept algebraically.
Leave answers in simplest radical form when necessary.
1) y = x2 - 8x - 7
.
2) y = x2 - 6x + 4
3) y = -2x2 - 8x + 5
4) Graph the equation f(x) =
x2 + 5x + 7 by finding the vertex, y-intercept,
and x-intercepts to the nearest tenth.
5) Graph y = -3x2 - 12x - 4 by completing the square
6) Graph y = 2x2 + 8x - 3 by using the quadratic formula
Using the Calculator
7) Graph y = -x2 + 3x - 1 using your calculator
To Find the X-Intercepts:
2ND
Trace
Zero
Go to the left and the right of one
of the zeros then repeat for the
other.
To Find the Vertex:
2nd
Trace
Min/Max
Go to the left and the right of the vertex.
To Find the Y-Intercept:
2nd
Trace
Value
Plug in 0 for x.
Confirm your answers algebraically:
Sum It Up!
When we cannot factor a quadratic we must use completing the
square or the quadratic formula to find the x-intercepts.
Be careful when plugging in the values to your calculator in order
to estimate.
HW #60 Answers
1. Vertex: (3, -3)
X-Int: (4.7,0)
(1.3,0)
Y-Int: (0, 6)
2. Vertex: (-5, -6.5)
X-Int: (-1.4,0)
(-8.6,0)
Y-Int: (0, 6)
4. Vertex: (-3/2, -15/2)
X-Int: (0.4,0)
(-3.4,0)
Y-Int: (0, -3)
3. Vertex: (-2, 7)
X-Int: (-4.6,0)
(0.6,0)
Y-Int: (0, 3)
Mixed Review:
1. (.05x - .7y)(.05x + .7y)
2. a(x-1)(x+1)(x2+1)(x4+1)