Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Octavio Chen 2022-03-24

Let $< a_{n} >$ and $< b_{n} >$ be the arithmetic progression sequences each with common difference 2 such that $a_{1} < b_{1}$ and let $c_{n} = \sum_{{k = 1}}^{n} a_{k}$ and $d_{n} = \sum_{{k = 1}}^{n} b_{k}$ . Suppose the points $A_{n} (a_{n}, c_{n})$ and $B_{n} (b_{n}, d_{n})$ are all lying on the parabola, $y = p x^{2} + q x + r$ , then find value of p, q.

mwombenizhjb 2022-03-24

Let p(x) be $a x^{2} - b x + c = 0$ where a,b,c are natural nos. and it has roots lying in the interval (1,2), then find the minimum value of a,b,c individually.

dayncNonow04r 2022-03-24

From $a x^{2} + b x + c$ (quadratic formula) 3 points (5,500),(3,375),(12,980) I solved
$25 a + 5 b + c = 500$
$9 a + 3 b + c = 375$
$144 a + 12 b + c = 980$
s it possible to solve it without a calculator (for the simulateneous equations) If yes, How can I do it?

markush35q 2022-03-23

Solve $z^{2} + (2 + 2 i) z + i = 0$

Deegan Chase 2022-03-23

Making sense of William Jones's solution of quadratic equations and notation
William Jones, when discussing quadratic equations, says: "Therefore if $\lor$ be put for the Sign of any Term, and ∧ for the contrary, all Forms of Quadratics with their Solutions, will be reduc'd to this one. If $x x \lor a x \lor b = 0$ then $\land \frac{1}{2} a \overset{―}{\pm a a \land b}!, ∣^{\frac{1}{2}}$ ."
Could you please help me make sense:
(a) What is meant with "the contrary" of "any sign"?
(b) Do I understand correctly that the "then" part supposed to be a solution to the preceding quadratic equation? If yes, how does this work exactly? How does it align with how we would symbolize the solution today?

sexoagotadorogyr 2022-03-23

Let $x^{2} - m x + 24$ be a quadratic with roots $x_{1} and x_{2}$ . If $x_{1} and x_{2}$ are integers, how many different values of m are possible?

talpajocotefnf3 2022-03-23

Let $x_{1} and x_{2}$ be the real root of the equation $x^{2} - k x + (k^{2} + 7 k + 15) = 0$ , if the maximum value of $(x_{1}^{2} + x_{2}^{2}) = d \frac{18}{x}$ , then find the value of x?

Lorelei Stanton 2022-03-23

Let $A (α) = (α I + (1 - α) B) - 1$ be the inverse of a convex combination of the n-by-n identity matrix I and a positive semidefinite symmetric matrix B, where the combination is given by $α \in (0, 1]$ . The matrix B is not invertible. For some n-dimensional vector c, I want to find $α$ such that
$c^{T} A (α) (I - B) A (α) c = 0$
Is there a closed-form solution for $α$ ?

Jazmyn Holden 2022-03-23

Let $\frac{1}{2} < \cos 2 A < 1$ and $6 \tan A - 6 \tan^{3} A = \tan^{4} A + 2 \tan^{2} A + 1$ , find $\tan 2 A$

Erik Cantu 2022-03-23

Let $α and β$ be the roots of $x^{2} - x - 1 = 0$ . If $P_{k} = {(α)}^{k} + {(β)}^{k}, k \geq 1$ then prove that
a) $P_{5} = 11 $$
b) $P_{1} + P_{2} + P_{3} + P_{4} + P_{5} = 26$

Isaac Hampton 2022-03-23

Let $α, β$ be the roots of $x^{2} - x + p = 0$ and $γ, δ$ be the roots of $x^{2} - 4 x + q = 0$
where p and q are integers. If $α, β, γ, δ$ are in GP then $p + q$ is?

Amya Horn 2022-03-23

Let $(x_{0}, y_{0})$ be the solution of the following equations ${(2 x)}^{\ln 2} = {(3 y)}^{\ln 3}, 3^{\ln x} = 2^{\ln y}$ . Then $x_{0}$ is:

Asher Olsen 2022-03-23

Given polynomial $P (x) = x^{2} + a x + b$ . Knowing that there only exists one value of real c such that $P^{2} (c) = c$ , calculate the minimum value of $a + b + c$ .
Notation: $P^{2} (x) = (P \circ P) (x)$

parksinta8rkv 2022-03-23

Given $\frac{z_{1}}{2 z_{2}} + \frac{2 z_{2}}{z_{1}} = i$ and 0, $z_{1}, z_{2}$ form two triangles with A,B the least angles of each. Find $\cot A + \cot B$ .

Octavio Chen 2022-03-22

Solve the given system of quadratic equations
$x^{2} + x y + x z = 2$
$y^{2} + y z + x y = 3$
$z^{2} + z x + y z = 4$

siliciooy0j 2022-03-22

Solve Surface Area Formula For Radius
Ok. I have a Surface Area Formula for a cylinder, but I am wanting to solve for the radius. The only information I have is the height of the cylinder, which is 8 inches. I know I can use the Quadratic Formula to convert the formula to solve for the radius, but I get stuck when doing the math.
$S A = 2 π r^{2} + 2 π r h$

rijstmeel7d4t 2022-03-22

Solve $\sqrt{x^{2} + 8 x + 7} + \sqrt{x^{2} + 3 x + 2} = \sqrt{6 x^{2} + 19 x + 13}$

ruililorNokmncf 2022-03-22

Let us consider some function $f (x, y) :, R^{2} \to R$ , such that
$\frac{\partial f (x, y)}{\partial x} = a, x + b, y \frac{\partial f (x, y)}{\partial y} = b, x + c, y f (0, 0) = 0$
where a, b, $c \in R$ .

nomadzkia0re 2022-03-22

Let $x^{2} - 2 x y - 3 y^{2} = 4$ Then find the range of $2 x^{2} - 2 x y + y^{2}$

swtda03u7bo 2022-03-22

Let $f (x) = x^{2} + a x + b$ . If for all non-zero real x
$f (x + \frac{1}{x}) = f (x) + f (\frac{1}{x})$
and the roots of $f (x) = 0$ are integers, what is the value of $a^{2} + b^{2}$ ?

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.

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