a. For the equation a x 2 + b x + c = 0 ( a ≠ 0 ) , the formula gives the solutions as x = _______________. b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________ a ≠ 0 . c. To apply the quadratic formula to solve the equation 8 x 2 − 42 x − 27 = 0 , the value of a is _____________, the value of b is _____________, and the value of c is __________. d. To apply the quadratic formula to solve the equation 3 x 2 − 7 x − 4 = 0 , the value of −-b is _____________ and the value of the radicand is _______________. e. The radicand within the quadratic formula is _________ and is called the ___________. f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers. g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers. h. Given a quadratic function f ( x ) = a x 2 + b x + c = 0 , the function will have no x -intercepts if the discriminant is (less than, greater than, equal to) zero.
a. For the equation a x 2 + b x + c = 0 ( a ≠ 0 ) , the formula gives the solutions as x = _______________. b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________ a ≠ 0 . c. To apply the quadratic formula to solve the equation 8 x 2 − 42 x − 27 = 0 , the value of a is _____________, the value of b is _____________, and the value of c is __________. d. To apply the quadratic formula to solve the equation 3 x 2 − 7 x − 4 = 0 , the value of −-b is _____________ and the value of the radicand is _______________. e. The radicand within the quadratic formula is _________ and is called the ___________. f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers. g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers. h. Given a quadratic function f ( x ) = a x 2 + b x + c = 0 , the function will have no x -intercepts if the discriminant is (less than, greater than, equal to) zero.
Solution Summary: The author explains the quadratic formula for the equation ax2+bx+c=0.
a. For the equation
a
x
2
+
b
x
+
c
=
0
(
a
≠
0
)
, the formula gives the solutions as
x
=
_______________.
b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________
a
≠
0
.
c. To apply the quadratic formula to solve the equation
8
x
2
−
42
x
−
27
=
0
, the value of a is _____________, the value of b is _____________, and the value of c is __________.
d. To apply the quadratic formula to solve the equation
3
x
2
−
7
x
−
4
=
0
, the value of −-b is _____________ and the value of the radicand is _______________.
e. The radicand within the quadratic formula is _________ and is called the ___________.
f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers.
g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers.
h. Given a quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
=
0
, the function will have no x-intercepts if the discriminant is (less than, greater than, equal to) zero.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Evaluate the following expression and show your work to support your calculations.
a). 6!
b).
4!
3!0!
7!
c).
5!2!
d). 5!2!
e).
n!
(n - 1)!
Amy and Samiha have a hat that contains two playing cards, one ace and one king. They are playing a game where they randomly pick a card out of the hat four times, with replacement.
Amy thinks that the probability of getting exactly two aces in four picks is equal to the probability of not getting exactly two aces in four picks. Samiha disagrees. She thinks that the probability of not getting exactly two aces is greater.
The sample space of possible outcomes is listed below. A represents an ace, and K represents a king. Who is correct?
Consider the exponential function f(x) = 12x. Complete the sentences about the key features of the graph.
The domain is all real numbers.
The range is y> 0.
The equation of the asymptote is y = 0
The y-intercept is 1
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