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3 years ago

Where is the location of the vertex of the parabola on a coordinate grid?

Mathematics

1 answer:

IrinaVladis [17]3 years ago

7 0

Answer:

below the x-axis

Step-by-step explanation:

y=x^2+2x-3

the vertex is located on the axis of symmetry

to find h ax^2 +bx+c

h= -b/2a = -2/2(1) = -1

the x coordinate of the vertex is -1

to find the y coordinate, substitute into the equation

y = (-1)^2 +2(-1) -3

= 1-2-3

= -4

(-1,-4)

the vertex is below the x axis

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Step-by-step explanation:

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Marianna [84]

You can use Heron's formula to solve this problem.

 $A= \sqrt{s(s-a)(s-b)(s-c)}$ , where A is the area; a,b,с are the sides; s is the semiperimeter of the triangle
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According to conditions:
a = x
b = x+1
с = 2x-1

Calculate the semiperimeter:
 $s= \frac{x+x+1+2x-1}{2} = \frac{4x}{2}=2x$

Now we can compose and solve the equation according to Heron's formula:
 $\sqrt{2x(2x-x)(2x-(x+1))(2x-(2x-1))}=x \sqrt{10} \\ \sqrt{2x(x)(2x-x-1)(2x-2x+1)}=x \sqrt{10} \\ \sqrt{2x^2(x-1)(1)}=x \sqrt{10} \\ \sqrt{2x^3-2x^2}=x \sqrt{10} \ \ \ |()^2 \\ 2x^3-2x^2=10x^2 \\ 2x^3-2x^2-10x^2=0 \\ 2x^3-12x^2=0 \ \ |:2 \\ x^3-6x^2=0 \\ x^2(x-6)=0 \\ \\ x^2=0 \\ x=0 \ \ \ \O \\ or \\ x-6=0 \\ x=6$

As a result, x = 6 is your answer.

I hope this helped.

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3 years ago