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Quadratic Equations have x2 (or some variable, squared) in them and are equations.
x2 + 5x + 6 = 0n2 – 7n = 18
2x2 = 11x + 40p2 = 16
(x + 7)(x + 2) = 0
The key to solving quadratic equations is the 0 property of multiplication If the product of two
quantities is 0, then one of
those quantities must be 0.
If a quadratic equation is factored, and says (__)(__) = 0:
The answers are the opposite of the factors.
Solve
(x + 7)(x – 1) = 0 x = -7 or 1
(x – 4)(x – 9) = 0 x = 4 or 9
(x + 8)(x + 13) = 0 x = -8 or -13
When there are coefficients, you can find the answers quickly by making a fraction, reading the factor backwards.
(9x – 13)(2x + 7) = 0
x = 13/9 or x = -7/2
If the equation isn’t factored.
1. Write it so it says ___ = 0.2. Factor.3. Do the opposite of the
factors.
If a quadratic equation doesn’t factor, there are many other ways it could possibly be solved. You’ll learn many of these in Geometry and in Advanced Algebra.
Quadratic Function Equation always has the
form f(x) = ax2 + bx + c The simplest quadratic
function is f(x) = x2
Graph f(x) = x2
Like the absolutevalue function, thisgives the sameanswers for positiveand negativenumbers.
This U-shaped graph is called a parabola. Many things in the real
world form parabola (arch)
shapes.
Quadratic functions are used particularly in problems involving Movement and the force of
gravity Area
What we usually care about with quadratic functions are the roots. These are the places
where the function = 0 They can also be called
“zeros” or “x-intercepts”.
Find the roots of
y = (x + 3)(x – 9)
f(x) = (x – 5)(x + 3)
g(x) = (x + 2)2
Just set the functions = 0
Find the roots:
f(x) = x2 + 11x + 28 (x + 7)(x + 4)
-7 and -4y = x2 – 11x + 18
(x – 9)(x – 2)9 and 2