Quadratic Function questions

Please complete the following questions. It is important that youshow all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.OPEN ENDED Choose two integers. Then write anequation with those roots in standard form. How would the equationchange if the signs of the two roots were switched?

OPEN ENDED Write a perfect square trinomialequation in which the linear coefficient is negative and the constantterm is a fraction. Then solve the equation.

Writing in Math Use the information onpage 273 to explain how to solve a quadratic equation using the ZeroProduct Property. Explain why you cannot solve x(x + 5) = 24 by solving x = 24 and x + 5 = 24. Page 273 is in the attachment Writing in Math Use the information onpage 281 to explain how complex numbers are related to quadraticequations. Explain how the a and c must be related if the equation ax2 + c = 0 has complex solutions and give the solutions of the equation 2×2 + 2 = 0. Page 281 is in the attachment Write quadratic
equations in
intercept form.
Solve quadratic
equations by
factoring.
100%
The intercept form of a quadratic equation is
y = 2(x – P)(X – 9). In the equation, p and 9
represent the x-intercepts of the graph
corresponding to the equation. The intercej
form of the equation shown in the graph is
y = 2(x – 1)(x + 2). The x-intercepts of the
graph are 1 and -2. The standard form of the
equation is y = 2×2 + 2x – 4.
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New Vocabulary
intercept form
FOIL method
Intercept Form Changing a quadratic equation in intercept form to
standard form requires the use of the FOIL method. The FOIL metho
uses the Distributive Property to multiply binomials.
KEY CONCEPT
FOIL Method for Multiplying Binomials
The product of two binomials is the sum of the products of F the first terms,
o the outer terms, I the inner terms, and L the last terms.
To change y = 2(x – 1)(x + 2) to standard form, use the FOIL method to
find the product of (x – 1) and (x + 2), x2 + x – 2, and then multiply
by 2. The standard form of the equation is y = 2×2 + 2x – 4.
You have seen that a quadratic equation of the form (x – P)(x – 1) = 0
has roots p and q. You can use this pattern to find a quadratic equation
for a given pair of roots.
Operations with Complex Numbers Consider 5 + 2i. Since 5 is a real number
and 2i is a pure imaginary number, the terms are not like terms and cannot be
combined. This type of expression is called a complaw numha
KEY CONCEPT
Complex Numbers
Words A complex number is any number that can be written in the form
a+bi, where a and b are real numbers and i is the imaginary unit.
a is called the real part, and b is called the imaginary part.
Examples 7 + 4i and 2 – 61 = 2 + (-6)i
The Venn diagram shows the complex numbers.
• If b = 0, the complex number is a real number.
• If b# 0, the complex number is imaginary.
• If a = 0, the complex number is a pure
imaginary number
Two complex numbers are equal if and only if
their real parts are equal and their imaginary
parts are equal. That is, a + bi = c + di if and
only if a = c and b = d.
Complex Numbers (a + bi)
Real Imaginary
Numbers Numbers
b=0 bo
Pure
Imaginary
Numbers
a = 0