Chapter 7, Problem 1VR

To determine

To fill: The blank provided in the statement, “The equation $x^2=2x-8$ is an example of a______ equation” with the correct options.

Answer to Problem 1VR

Solution:

The complete statement is, “The equation $x^2=2x-8$ is an example of a quadratic equation”.

Explanation of Solution

Given information:

The provided options are,

$\left(a\right)$ Complete

$\left(b\right)$ Parabola

$\left(c\right)$ Line

$\left(d\right)$ Discriminant

$\left(e\right)$ Symmetry

$\left(f\right)$ Linear

$\left(g\right)$ Polynomial

$\left(h\right)$ Quadratic

$\left(i\right)$ Rational

$\left(j\right)$ Vertex

And,

$\left(k\right)$ x-intercept

$\left(l\right)$ y-intercept

The quadratic equation is the equation of the type $a{x}^2+bx+c=0$.

Where $a,b$ and c are real number constants and $a\ne 0$.

Here, the provided equation is $x^2=2x-8$.

The equation written in $a{x}^2+bx+c=0$ form as,

Subtract $2x-8$ from both sides of the equation $x^2=2x-8$,

$\begin{array}{l}{x}^2-2x+8=2x-8-2x+8\\ x^2-2x+8=0\end{array}$

The resultant equation is $x^2-2x+8=0$, which is $a{x}^2+bx+c=0$ form.

Thus, verified.

Hence the complete statement is, “The equation $x^2=2x-8$ is an example of a quadratic equation”.