Maths-

General

Easy

Question

Rewrite the equation as a system of equations, and then use a graph to solve.
$4 x squared equals 2 x minus 5$

hint Hint:

A set of equation can be solved by graphing them. Each points of intersection among the graphs are solutions for the given set. If there are no points of intersection, then there are no solutions for the set.
We are asked to rewrite the equation into a system of equation and then use a graph to solve.

The correct answer is: We are asked to rewrite the equation into a system of equation and then use a graph to solve.

Step 1 of 3:
Equate each side of the equation to a new variable, y. Thus, we have:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 4 x squared space space space space end cell row cell y equals 2 x minus 5 end cell end table$
Step 2 of 3:
Find two coordinate points of the equation, y = 2x - 5
when x = 1,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 left parenthesis 1 right parenthesis minus 5 end cell row cell y equals 2 minus 5 space space space space space end cell row cell y equals negative 3 space space space space space space space space end cell end table space$
when x = -1,
$table attributes columnalign right columnspacing 0em end attributes row cell straight y equals 2 left parenthesis negative 1 right parenthesis minus 5 end cell row cell straight y equals negative 2 minus 5 space space space space space end cell row cell straight y equals negative 7 space space space space space space space space space space space space end cell end table$
The required points are, (1,-3) and (-1,-7)
Find three coordinate points of the equation, y = 4x2
when x = -1,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 4 x squared space space space space space space end cell row cell y equals 4 left parenthesis negative 1 right parenthesis squared end cell row cell y equals 4 left parenthesis 1 right parenthesis space space space space space space end cell row cell y equals 4 space space space space space space space space space space space end cell end table$
when x = 1,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 4 x to the power of 2 space space end exponent end cell row cell y equals 4 left parenthesis 1 right parenthesis squared end cell row cell y equals 4 left parenthesis 1 right parenthesis space space space end cell row cell y equals 4 space space space space space space space end cell end table$
when x =0,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 4 x squared space space end cell row cell y equals 4 left parenthesis 0 right parenthesis squared end cell row cell y equals 0 space space space space space space end cell end table$
The required points are: (-1, 4),(1, 4) and (0, 0)
Step 3 of 3:
Draw the graph of the set of equations, corresponding to the found points.

It is clear that there are no points of intersection. Hence, the given equation has no solution.

Maximum solutions possible for a quadratic equation are two. There are instances where the equation has no solutions as well.

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Rewrite the equation as a system of equations, and then use a graph to solve.

The correct answer is: We are asked to rewrite the equation into a system of equation and then use a graph to solve.

Related Questions to study

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Rewrite the equation as a system of equations, and then use a graph to solve.
$4 x squared equals 2 x minus 5$

Find the solution of the system of equations.
$y equals 2 x squared plus 5 x minus 30$
y = 2x + 5

Find the solution of the system of equations.
$y equals 2 x squared plus 5 x minus 30$
y = 2x + 5

Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”

Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”

Find the solution of the system of equations.
$y equals 3 x squared plus 2 x plus 1$
$y equals 2 x plus 1$

Find the solution of the system of equations.
$y equals 3 x squared plus 2 x plus 1$
$y equals 2 x plus 1$

Find the solution of the system of equations.
$y equals x squared plus 8 x plus 30$
y = 5 - 2x

Find the solution of the system of equations.
$y equals x squared plus 8 x plus 30$
y = 5 - 2x

Find the solution of the system of equations.
$y equals x squared plus 6 x plus 9$
y = 3x

Find the solution of the system of equations.
$y equals x squared plus 6 x plus 9$
y = 3x

Find the solution of the system of equations.
$y equals x squared minus 5 x minus 8$
$y equals negative 2 x minus 4$

Find the solution of the system of equations.
$y equals x squared minus 5 x minus 8$
$y equals negative 2 x minus 4$

Consider this simple bivariate data set.

a) Draw a scatter plot for the data.
b) Describe the correlation between x and y as positive or negative.
c) Describe the correlation between x and y as strong or weak.
d) Identify any outliers.

Consider this simple bivariate data set.

a) Draw a scatter plot for the data.
b) Describe the correlation between x and y as positive or negative.
c) Describe the correlation between x and y as strong or weak.
d) Identify any outliers.