Describe the graph of a quadratic function whose related quadratic equation has no real solutions.

a2linetagadaW
2021-08-15
Answered

Describe the graph of a quadratic function whose related quadratic equation has no real solutions.

You can still ask an expert for help

Benedict

Answered 2021-08-16
Author has **108** answers

Consider the quadratic function:

$y=a{x}^{2}+bx+c$

The solutions of the quadratic equation$y=a{x}^{2}+bx+c$ are coincide with values of x where the graph of the quadratic function $y=a{x}^{2}+bx+c$ intersects the x-axis.

If the graph of the quadratic function does not intersect the x-axis the the quadratic equation has no solution.

In this case the graph is either below the x-axis or obove the x-axis and does not touch the x-axis.

The solutions of the quadratic equation

If the graph of the quadratic function does not intersect the x-axis the the quadratic equation has no solution.

In this case the graph is either below the x-axis or obove the x-axis and does not touch the x-axis.

Jeffrey Jordon

Answered 2022-01-14
Author has **2581** answers

Answer is given below (on video)

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Find a such that $\left\{{x}_{1}\right\}}^{2}+{\left\{{x}_{2}\right\}}^{2$ takes the minimal value where $x}_{1},{x}_{2$ are solutions to ${x}^{2}-ax+(a-1)=0$ .

asked 2022-01-20

How to find the formula of a quadratic function knowing that it contains the points $(-2,\text{}2)$ and $(0,\text{}1)$ and $(1,\text{}-2.5)$ ?

asked 2022-11-14

Find the form of f(x, y) knowing the form of contour lines in the XZ and YZ planes

I am trying to find the form of $z=f(x,y)$. I know that:

Contour lines in the XZ plane are of the form:

$z=A\ast ln(x)+B$

(the A and B parameters vary with y)

Contour lines in the YZ plane are of the form:

$z=C{y}^{2}+Dy+E$

(the C, D and E parameters vary with x)

What is then the form of $z=f(x,y)$?

I am trying to find the form of $z=f(x,y)$. I know that:

Contour lines in the XZ plane are of the form:

$z=A\ast ln(x)+B$

(the A and B parameters vary with y)

Contour lines in the YZ plane are of the form:

$z=C{y}^{2}+Dy+E$

(the C, D and E parameters vary with x)

What is then the form of $z=f(x,y)$?

asked 2022-01-22

How do you find the solution to the quadratic equation ${x}^{2}-4x-3=0$ ?

asked 2022-04-24

How can we prove there are infinitely many solutions to $\frac{1}{{x}^{2}-2x+3}=y$ by only staying at Further maths at High School level? Will the graph ever go below the x-axis or will stay on it?

asked 2022-11-20

Alternative for calculating the nth of quadratic sequence

Given the quadratic sequence

$f(n)=1,7,19,37,\cdots $

To calculate the f(n) for $n\ge 1$.

$f(n)=a{n}^{2}+bn+c$

We start with the general quadratic function, then sub in for $n:=1,2$ and 3

$f(1)=a+b+c$

$f(2)=4a+2b+c$

$f(3)=9a+3b+c$

Now solve the simultaneous equations

$\begin{array}{}\text{(1)}& a+b+c=1\end{array}$

$\begin{array}{}\text{(2)}& 4a+2b+c=7\end{array}$

$\begin{array}{}\text{(3)}& 9a+3b+c=19\end{array}$

$(2)-(1)$ and $(3)-(2)$

$\begin{array}{}\text{(4)}& 3a+b=6\end{array}$

$\begin{array}{}\text{(5)}& 5a+b=12\end{array}$

$(5)-(4)$

$a=3$

$b=-3$

$c=1$

$f(n)=3{n}^{2}-3n+1$

This method is very long. Is there another easy of calculating the f(n)?

Given the quadratic sequence

$f(n)=1,7,19,37,\cdots $

To calculate the f(n) for $n\ge 1$.

$f(n)=a{n}^{2}+bn+c$

We start with the general quadratic function, then sub in for $n:=1,2$ and 3

$f(1)=a+b+c$

$f(2)=4a+2b+c$

$f(3)=9a+3b+c$

Now solve the simultaneous equations

$\begin{array}{}\text{(1)}& a+b+c=1\end{array}$

$\begin{array}{}\text{(2)}& 4a+2b+c=7\end{array}$

$\begin{array}{}\text{(3)}& 9a+3b+c=19\end{array}$

$(2)-(1)$ and $(3)-(2)$

$\begin{array}{}\text{(4)}& 3a+b=6\end{array}$

$\begin{array}{}\text{(5)}& 5a+b=12\end{array}$

$(5)-(4)$

$a=3$

$b=-3$

$c=1$

$f(n)=3{n}^{2}-3n+1$

This method is very long. Is there another easy of calculating the f(n)?