Lesson 612 of 1524
Quadratic Equations and Functions
Binomial Squares Pattern If a and b are real numbers,
Practice this chapterBinomial Squares Pattern If a and b are real numbers, Square Root Property If x 2 = k , then x = k or x = - k or x = ± k
Isolate the quadratic term and make its coefficient one Find ( 1 2 b ) 2 , the number to complete the square
quadratic function — A quadratic function, where a , b , and c are real numbers and a ≠ 0 , is a function of the form f ( x ) = a x 2 + b x + c. discriminant — In the Quadratic Formula, x = - b ± b 2 - 4 a c 2 a , the quantity b 2 - 4 ac is called the discriminant. quadratic inequality — A quadratic inequality is an inequality that contains a quadratic expression.
Be able to graph a quadratic function in the vertex form f ( x ) = a ( x - h ) 2 + k using properties Step 1. Rewrite the function in f ( x ) = a ( x - h ) 2 + k form; solve a Quadratic Inequality Graphically Step 1. Write the quadratic inequality in standard form.
Worked example
What does “quadratic function” mean in Quadratic Equations and Functions?
- 1Use the wording this chapter gives for quadratic function.
- 2The book says: A quadratic function, where a , b , and c are real numbers and a ≠ 0 , is a function of the form f ( x ) = a x 2 + b x + c.
- 3Do not use the meaning of discriminant. That term means In the Quadratic Formula, x = - b ± b 2 - 4 a c 2 a , the quantity b 2 - 4 ac is called the discriminant.
Result: A quadratic function, where a , b , and c are real numbers and a ≠ 0 , is a function of the form f ( x ) = a x 2 + b x + c
Why. That is the meaning this chapter gives for quadratic function.
Do not swap quadratic function and discriminant. quadratic function means A quadratic function, where a , b , and c are real numbers and a ≠ 0 , is a function of the form f ( x ) = a x 2 + b x + c. discriminant means In the Quadratic Formula, x = - b ± b 2 - 4 a c 2 a , the quantity b 2 - 4 ac is called the discriminant.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.