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How is the vertex form of an equation different from the standard form and what values change the shape of the graph?
The vertex form of a quadratic equation is expressed as ( y = a(x-h)^2 + k ), where ((h, k)) is the vertex of the parabola, while the standard form is ( y = ax^2 + bx + c ). In vertex form, the values of (a), (h), and (k) directly influence the shape and position of the graph; specifically, (a) determines the width and direction of the parabola, while (h) shifts it horizontally and (k) shifts it vertically. Changes to (a) affect the steepness, while altering (h) and (k) moves the vertex without changing the graph's shape.
What else can I help you with?
What can be said of an ellipse when the two denominator values in its standard equation are the same?
When the two denominator values in the eclipse standard equation are the same, it can be said to be in foci.
What does a variable do in a math problem?
Variables in a math problem vary or change. If in an equation, different variables change values depending on constants, evanuations, etc. For example: in y = x + 2, y can be any number as long as x is that number plus two. The varibles in this equation change value but are defined by the equation.
What are the letters in an equation called?
The letters in an equation are called variables. They represent unknown values or quantities that can change. In addition to variables, equations may also include constants, which are fixed values. Together, they help express relationships between different quantities in mathematical expressions.
Is a letter symbol that represents a quantity that can change?
Yes, a letter symbol that represents a quantity that can change is called a variable. In mathematics and programming, variables are used to hold different values and can be manipulated in various operations. For example, in the equation (x + 2 = 5), (x) is a variable that can take on different values.
What is the different between equation and inequality?
An equation is a mathematical that asserts theequality of two expressions. An inequality is a relation that holds between two values when they are different.
What can be said of an ellipse when the two denominator values in its standard equation are the same?
When the two denominator values in the eclipse standard equation are the same, it can be said to be in foci.
How is constant found?
The constant in a mathematical equation can be found by determining the value of the term that does not change across different values of the variable. This can be done by solving the equation for different values of the variable and isolating the term that remains the same.
What can be said of an ellipse when the two denominator values in its standard equation are the same-?
it becomes a circle
What does a variable do in a math problem?
Variables in a math problem vary or change. If in an equation, different variables change values depending on constants, evanuations, etc. For example: in y = x + 2, y can be any number as long as x is that number plus two. The varibles in this equation change value but are defined by the equation.
What are the letters in an equation called?
The letters in an equation are called variables. They represent unknown values or quantities that can change. In addition to variables, equations may also include constants, which are fixed values. Together, they help express relationships between different quantities in mathematical expressions.
Is a letter symbol that represents a quantity that can change?
Yes, a letter symbol that represents a quantity that can change is called a variable. In mathematics and programming, variables are used to hold different values and can be manipulated in various operations. For example, in the equation (x + 2 = 5), (x) is a variable that can take on different values.
What equation is true for some values of its variable and is not true for others?
No equation can have that property. It cannot be an equation if it is not true. If necessary, the domain must be amended. An equation can have different forms over different parts of its domain.
What is the different between equation and inequality?
An equation is a mathematical that asserts theequality of two expressions. An inequality is a relation that holds between two values when they are different.
What does each letter in the equation stand for?
In an equation, the letters represent variables that can take on different values. Each letter represents a specific quantity or value that is being referred to in the equation. The goal is to solve for these variables to determine their values and make the equation true.
Why would you want to solve a literal equation for a variable when you could simply plug in known values and then solve the resulting linear equation?
if you solve by plugging in the known values ahead of time you won't have a general formula for the variable in the literal equation. Therefor if the known values change, you would have to start all over again, making each problem more individualized. Once the literal equation is solved for some variable, if the known values change all you have to do is plug in those new numbers to your literal equation, and out pops your answer
How do you solve an equation with the same variable on both sides?
The variables may have different values.
Is there an explicit solution to a single linear equation with two variables?
Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions.
