Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

hapantad2j 2022-04-24

If two tangents can be drawn to different tangents of a hyperbola $\frac{x^{2}}{1} - \frac{y^{2}}{4} = 1$ from the point $(a, a^{2})$ , then find range of a

Halle Marsh 2022-04-24

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

Gage Potter 2022-04-24

If the roots of the quadratic equation
$(4 p - p^{2} - 5) x^{2} - (2 p - 1) x + 3 p = 0$
lie on either side of unity, then the number of integral values of p is?

bacasauvfl 2022-04-24

If real a and b satisfy $17 (a^{2} + b^{2}) - 30 a b - 16 = 0$ then find the maximum value of $\sqrt{16 a^{2} + 4 b^{2} - 16 a b - 12 a + 6 b + 9}$

Maeve Bowers 2022-04-24

If roots of the equation $a x^{2} + b x + c = 0$ are $α, β$ , find roots of equation $a c x^{2} - b (c + a) x + {(c + a)}^{2} = 0$ in terms of $α, β$ .

markjasonvictorio69 2022-04-24

X14 and x2

Ezequiel Olson 2022-04-24

Simultaneous Equations Finding the Intersection of a Cubic and a Quadratic
My functions are
$y = - 0.65 {(x - 8.165)}^{2} + 1.5 (x - 8.165) + 6.872$
$y = 0.08 {(x - 11)}^{3} - 2.2 (x - 11) + 5.9$
By using simultaneous equations and equating the functions to one another I've simplified it to the point where:
$0.08 x^{3} - 1.99 x^{2} + 14.7255 x - 27.608 = 0$
This had me stuck for a while but when I looked it up online I found I could use the Newton - Raphson Method to solve it.
I got the intercepts: $x = 2.85281, x = 10.98682, x = 11.03536$
And although this helped me greatly, for the assignment I'm doing I won't be marked on using that method as we haven't been taught it and it's not on the criteria.
I'm just wondering if there is another method I can use that would get the same results.

Dashawn Clark 2022-04-24

Proof by contradiction: $n^{3} - n - 6 = 0$ means $m^{3} - m - 6 \neq 0$ when $m \neq n$

airesex2 2022-04-23

Is it valid to write, ${| x - y |}^{2} = {| x |}^{2} + {| y |}^{2} - 2 | x | | y |$ ?

Kailey Perez 2022-04-23

Inequality with two variables
For x, $y \in R$ , find the maximum of
$P = \frac{2 x y (x y + 1) + (x + y) (x y - 1)}{(1 + x^{2}) (1 + y^{2})}$

tonnithrkr 2022-04-23

If x and y are real numbers and $x^{2} + y^{2} - 4 x - 6 y - 1 = 0$ what is the minimum value of $x + y$ ?

bacasauvfl 2022-04-23

If the roots $α and β$ of the equation, $x^{2} - \sqrt{2} x + c = 0$ are complex for some real numbers $c \neq 1$ and $| \frac{α - β}{1 - α β} | = 1$ then a value of c is

kadetskihykw 2022-04-23

If two tangents can be drawn to distinct branches of hyperbola $x^{2} - \frac{y^{2}}{4} = 1$ from the point $(a, a^{2})$ , then pick the options
1) $a \in (- 2, 0)$
2) $a \in (0, 2)$
3) $a \in (- \infty, - 2)$
4) $a \in (\infty, 2)$

Hugh Walls 2022-04-23

If the given quadratic equation has two integral roots $α and β$ then find $α + β and | α - β |$
$x^{2} - \frac{(α^{2} + 11) x}{9} + \frac{15}{4} (α + β) + 16 = 0 .$

abiejose55d 2022-04-23

If the coefficients of a quadratic equation are odd numbers, show that it cannot have rational roots
$a x^{2} + b x + c = 0$

Dania Robbins 2022-04-23

If $p = \frac{1}{3} + \frac{1}{3} \frac{3}{6} + \frac{1}{3} \frac{3}{6} \frac{5}{9} + \dots$
and $p^{2} + a p + c = 0 .$
Find a, c also $| c | = 2$ .

Troszokd95 2022-04-23

If $N = y^{2} + 1$ then the continued fraction of $\sqrt{N}$ has period 1. i.e. $\sqrt{N} = [q_{0}; \overset{―}{q_{1}}]$ or similarly
$x = q_{0} + c \frac{1}{q_{1} + c \frac{1}{q_{1} + c \frac{1}{q_{1} + \dots}}}$

Eileen Garza 2022-04-23

If $f (x) = {(x^{2} + 2 α x + α^{2} - 1)}^{\frac{1}{4}}$ has its domain and range so that union is R, what does $α$ satisfy?

acceloq3c 2022-04-23

Showing that $x^{n} - a x^{n - 1} - b x - 1$ , for non-negative integers $n \geq 3, a \geq 1$ , b, has no double roots

Kymani Shepherd 2022-04-23

How could I find x in this equation
$x^{2} - x + 6 \equiv 0 \pm \mod 9$

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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