Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Hallie Watts 2022-04-19

What are the steps to factor $x^{2} - 1$ into $(x + 1) (x - 1)$ ?

bacasauvfl 2022-04-19

Solve
${(4 + \sqrt{15})}^{x} + {(4 - \sqrt{15})}^{x} = 62$

Aldo Fernandez 2022-04-18

What is the condition for real roots?
Given that the equation in x has at least a real root, find the range of m:
$(m^{2} - 1) x^{2} - 2 (m + 2) x + 1 = 0$

Gustavo Lam 2022-04-18

What is ${(3 + w + 2 w^{2})}^{4}$ ?
where w is cube roots of unity
We know that $1 + w + w^{2} = 0$ , so
${(3 - 1 - w^{2} + 2 w^{2})}^{4}$ or, ${(2 + w^{2})}^{4}$
How can I progress after this. Every suggestion will be appreciated.

Hallie Watts 2022-04-18

How do we find the range of an algebraic rational function of the form $\frac{a_{1} x^{2} + b_{1} x + c_{1}}{a_{2} x^{2} + b_{2} x + c_{2}}$
for real values of x?

Gretchen Barker 2022-04-18

How do I solve
$c^{2} + 1 > 2 c - 1$ when $c \geq 2$ ?

Rachael Velasquez 2022-04-17

What can a translation of $y = x - e$ do to bring a polynomial into a depressed form?

Frances Simon 2022-04-17

How do we find out the discriminant for this quadratic equation?
$(a + c) a x^{2} + 2 b x + c = 2 (a c - b^{2}) (x^{2} + 1)$
If I bring the RHS to LHS and then expand , it will take a lot of time for me to first expand and then find the discriminant for this equation whence is the first way to find the discriminant. Is there a quicker way with which I can find its discriminant ? Maybe just by looking at the equation , not even have to expand.

Ansley Sparks 2022-04-16

Modelling the orchard yields with diminishing returns per tree
Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 4 apples per tree (i.e., the yield per tree will decrease by 4 apples). How many trees should she have in the orchard to maximize her production of apples?

Miguel Hanson 2022-04-16

Minimum value of
$\sqrt{x^{4} + 3 x^{2} - 6 x + 10} + \sqrt{x^{4} - 5 x^{2} + 9}$ without using calculus?

Leonard Montes 2022-04-16

Math Olympiad question:If the equation in x has real roots, then find the value of a and b.
$x^{2} + 2 (1 + a) x + (3 a^{2} + 4 a b + 4 b^{2} + 2) = 0$

Zane Decker 2022-04-16

Let f(x) be a quadratic function and c constant. Which of the following statements is correct?
a) There is a unique value of c such that y = f(x) - c has a double root.
b) There is unique value of c such that y = f(x-c) has a double root.

Leia Sullivan 2022-04-16

Let be A a real $N \times N$ matrix and X a real $N \times 1$ matrix.
1. If $X^{T} \cdot A \cdot X = 0$ and $det (A) = 0$ , this implies necessarially that $A \cdot X = 0$ ?
2. If $X^{T} \cdot A \cdot X = 0$ and $det (A) \neq 0$ , exists a condiction to that $A \cdot X = 0$ be true?

Mina Whitehead 2022-04-16

Is there a quicker way to calculate the square of quadratic polynomial?
${(x^{2} - 6 x + 7)}^{2}$

Angela Harrell 2022-04-16

Is there a method to factor equations with two variables raised to the second power?
I found the equation $2 b^{2} - a b - a^{2} = 0$ on a problem and couldn't find a way to factor it. Is there any method to factor these types of equations?

Alan Zavala 2022-04-16

What is the condition that the following equation has four real roots?
$(a_{1} x^{2} + b_{1} x + c_{1}) (a_{2} x^{2} + b_{2} x + c_{2}) = 0$
a. $c_{1} c_{2} > 0$
b. $a_{1} c_{2} < 0$
c. $a_{2} c_{1} < 0$

Leonard Montes 2022-04-15

Minimum value when
$a b c + a b + 4 b c + 9 c a = 144$

Charlotte Holden 2022-04-15

Let A,B,C be strictly positive real numbers satisfying $A + B + C = 1$ and let a,b,c be real variables. Suppose a,b,c satisfy the following system of equations: $\frac{A^{2}}{a} + \frac{B^{2}}{b} + \frac{C^{2}}{c} = 1, and a + b + c = 1 .$

Heather Dickson 2022-04-15

Is $x^{2} - a x + a^{x} - 1$ real and less than 2?

zdebe5l8 2022-04-15

Is $f (x) = x^{2} - 13 \sqrt{x} + 30 a$ quadratic?

Finding a reliable quadratic function solver is quite popular today as students look for answers to equations that they encounter during those Algebra tasks. Still, quadratic function examples with answers are not so common, which is why we have collected related questions and answers for you to help you find various solutions and learn. Take your time to explore quadratic function questions. If you manage to understand at least one quadratic function solution, you will understand all the rest because it is exactly how things work. Even the most complex quadratic function equation makes sense when you have an example.

Algebra I

Quadratic Function Real Life Examples and Applications