if you mean the zeroes, then I'd say they are at about (-5,0) and (6,0) making the equation
y = a(x+5)(x-6)
To find a, note that the y-intercept is at about (0,-30) so that means that
-25a = -30
a = 6/5
So, y = 6/5 (x+5)(x-6)
If by "solution" you mean something else, then you need to explain just what you want.
What is the solution for the quadratic equation depicted in the graph?
i.imgur.com/gCqO8iE.gif
2 answers
The solution is where y = 0
It is obvious from the figure that one solution is x = 6
I assume (because it is not indicated on the graph) that the second solution is x = - 5 because:
[ - 4 + ( - 6 ) ] / 2 = ( - 4 - 6 ) / 2 = - 10 / 2 = - 5
The roots are x = 6 and x = - 5
Each quadratic equation can be written in the form:
y = a x² + b x + c = a ( x - x1 ) ( x - x2 )
If the solutions are x = 6 and x = - 5 then the quadratic equation is given:
y = a x² + b x + c = a ( x - x1 ) ( x - x2 ) = a ( x - 6 ) [ x - ( - 5 ) ]
y = a ( x - 6 ) ( x + 5 )
The coefficient a can be determined from the conditions x = - 4, y = - 10 ( which can be seen in the diagram ).
put x = - 4 and y = - 10 in the equation:
y = a ( x - 6 ) ( x + 5 )
- 10 = a ( - 4 - 6 ) ( - 4 + 5 )
- 10 = a ∙ ( - 10 ) ∙ 1
- 10 = - 10 a
Divide both sides by - 10
1 = a
a = 1
y = 1 ∙ ( x - 6 ) ( x + 5 )
y = ( x - 6 ) ( x + 5 )
y = x ∙ x - 6 ∙ x + 5 ∙ x - 6 ∙ 5
y = x² - 6 x + 5 x - 30
y = x² - x - 30
y = a x² + b x + c
The coefficients of your equation are:
a = 1 , b = - 1 , c = - 30
The vertex is the lowest point on the parabola if the parabola opens upward and is the highest point on the parabola if the parabola opens downward.
x coordinate of the vertex is:
xv = - b / 2 a
In this case:
xv = - ( - 1 ) / 2 ∙ 1 = 1 / 2
xv = 0.5
yv = ( 1 / 2 )² - 1 / 2 - 30
yv = 1 / 4 - 1 / 2 - 30
yv = - 1 / 4 - 120 / 4
yv = - 121 / 4
yv = - 30.25
Therefore, the vetex is not visible in the graph because the lowest point is drawn on the graph y = - 30
So your function is:
y = x² - x - 30
The roots are ( - 5 , 0 ) , ( 6 , 0 )
The vertex is ( 0.5 , - 30.25 )
It is obvious from the figure that one solution is x = 6
I assume (because it is not indicated on the graph) that the second solution is x = - 5 because:
[ - 4 + ( - 6 ) ] / 2 = ( - 4 - 6 ) / 2 = - 10 / 2 = - 5
The roots are x = 6 and x = - 5
Each quadratic equation can be written in the form:
y = a x² + b x + c = a ( x - x1 ) ( x - x2 )
If the solutions are x = 6 and x = - 5 then the quadratic equation is given:
y = a x² + b x + c = a ( x - x1 ) ( x - x2 ) = a ( x - 6 ) [ x - ( - 5 ) ]
y = a ( x - 6 ) ( x + 5 )
The coefficient a can be determined from the conditions x = - 4, y = - 10 ( which can be seen in the diagram ).
put x = - 4 and y = - 10 in the equation:
y = a ( x - 6 ) ( x + 5 )
- 10 = a ( - 4 - 6 ) ( - 4 + 5 )
- 10 = a ∙ ( - 10 ) ∙ 1
- 10 = - 10 a
Divide both sides by - 10
1 = a
a = 1
y = 1 ∙ ( x - 6 ) ( x + 5 )
y = ( x - 6 ) ( x + 5 )
y = x ∙ x - 6 ∙ x + 5 ∙ x - 6 ∙ 5
y = x² - 6 x + 5 x - 30
y = x² - x - 30
y = a x² + b x + c
The coefficients of your equation are:
a = 1 , b = - 1 , c = - 30
The vertex is the lowest point on the parabola if the parabola opens upward and is the highest point on the parabola if the parabola opens downward.
x coordinate of the vertex is:
xv = - b / 2 a
In this case:
xv = - ( - 1 ) / 2 ∙ 1 = 1 / 2
xv = 0.5
yv = ( 1 / 2 )² - 1 / 2 - 30
yv = 1 / 4 - 1 / 2 - 30
yv = - 1 / 4 - 120 / 4
yv = - 121 / 4
yv = - 30.25
Therefore, the vetex is not visible in the graph because the lowest point is drawn on the graph y = - 30
So your function is:
y = x² - x - 30
The roots are ( - 5 , 0 ) , ( 6 , 0 )
The vertex is ( 0.5 , - 30.25 )
2 answers