Solving an absolute value equation and the defference between two quadratics

In summary, an absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on a number line. To solve an absolute value equation, the equation must be split into two separate equations, one with the positive value of the absolute value expression and one with the negative value. The difference between two quadratics is the different values for the constants a, b, and c, which leads to different shapes and positions of the parabolas. To solve a quadratic equation, you can use the quadratic formula, factor the equation, or complete the square. Absolute value equations can be applied in real-life situations, such as solving problems involving distance, speed, and time, or in physics for problems involving
  • #1
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Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

9) Solve for all X: |2x-5| + 3 = 18

My Answer: x = 10, x = -5

10) Subtract and simplify: (5x^2 - 3x + 8) - (-4x^2 - x + 10)

My Answer: 9x^2 - 2x - 2
 
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  • #2
Re: Please check my answers - 5

9.) Correct.

I would be inclined to write this equation as:

\(\displaystyle |x-2.5|=7.5\)

Now we can see that $x$ is a number whose distance from 2.5 is 7.5 units, or:

\(\displaystyle x=2.5\pm7.5\implies x=-5,\,10\)

10.) Correct.
 

FAQ: Solving an absolute value equation and the defference between two quadratics

What is an absolute value equation?

An absolute value equation is an equation that contains an absolute value expression. The absolute value of a number is its distance from zero on a number line. In an absolute value equation, the variable can have two possible values that satisfy the equation.

How do you solve an absolute value equation?

To solve an absolute value equation, you must first isolate the absolute value expression on one side of the equation. Then, split the equation into two separate equations, one with the positive value of the absolute value expression and one with the negative value. Solve each equation separately to find the possible values of the variable.

What is the difference between two quadratics?

A quadratic equation is an equation with the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The difference between two quadratics is that they have different values for the constants a, b, and c. This leads to different shapes and positions of the parabolas.

How do you solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. You can also factor the equation or complete the square to solve for the variable.

How do you apply absolute value equations in real-life situations?

Absolute value equations can be used to solve problems involving distance, speed, and time. For example, if you are traveling at a constant speed and need to know how long it will take to reach a destination, you can use an absolute value equation to solve for the possible times. Additionally, absolute value equations can be used in physics to solve problems involving acceleration and displacement.

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