Solving Quadratics
Solve: x2 −4 = 0
X=2
X=-2
What is the axis of symmetry of y= x2 −6x +4?
x= 3
What number completes the square in
x2 + 6x + __?
9, because
(6/2)2=9
** (b/2)2 **
Define "coefficient" and explain how it differs from a constant.
A coefficient is the number in front of a variable; a constant is a term without a variable.
What is the leading coefficient of -5x +7 +3x2 ?
3
Solve: x2− 5x +6 =0
x=2
x=3
Find the vertex of y= x2 +4x −5
Vertex: (−2,−9)
Solve: x2 +4x +4 =9
x= 1
x= -5
What is a polynomial? How do you classify one by degree and number of terms?
A polynomial is an expression with terms connected by addition or subtraction. Classified by degree (linear, quadratic, cubic, etc.) and number of terms (monomial, binomial, trinomial).
If the leading coefficient is positive, what does this tell us?
If positive, the parabola opens up.
Solve: x2 +2x −8 =0
x=-4
x=2
What is the significance of the axis of symmetry in a quadratic graph?
The axis of symmetry splits the parabola into two equal halves.
Solve: x2 −8x +16 =25
x=9
x=-1
Define "binomial" and give an example where the terms have different exponents.
A binomial is a polynomial with two terms, such as x2+3x.
What is the relationship between the axis of symmetry and the vertex of a quadratic function?
The axis of symmetry is the vertical line that passes through the vertex, splitting the parabola into two halves.
Solve by factoring: x2 −7x +10 =0
x=2
x=5
The graph of a quadratic equation has an axis of symmetry at x=−3.
If one solution to the equation is x=2, what is the other solution?
x=-8
-3-5=8
Complete the square to solve for x.
x2+6x=7.
x= -7
x= 1
Explain the difference between like terms and unlike terms,
Like terms have the same variable and exponent (e.g., 3x2 and −5x2).
Unlike terms have different variables or exponents (e.g., 4x2 and −2x).
Compare the graphs of y=2x2 and y=−2x2
The graph of y=2x2 has a minimum and opens up
The graph y=−2x2 has a maximum and opens down.
Solve for X
5x3 -25x2 -30x
5x (x-6) (x+1)
x=0 x=6 x=-1
How can the axis of symmetry of a quadratic function be found using only the standard form equation
y= ax2+ bx +c
x=(-b/2a)
Solve x2 −10x +21 =0
by completing the square.
x=3 and x=7
What are all the names for the x-intercepts?
X-intercepts, roots, solutions, zeros.
What is the difference between the leading coefficient quadratic function and a quartic function?
The leading coefficient for a quadratic function is in the form of ax2.
The leading coefficient for a quartic function is in the form of ax4.