Kaylaciffelt
Answered

Drag each label to the correct location on the table.
Match each equation with its number of unique solutions.
y = 3x^2- 6x + 3
y= -x^2 - 4x + 7
y = -2x^2 + 9x – 11

Answer :

caitlynm2395

Answer:

1. 1 real solution

2. 2 real solutions

3. Two complex solutions

Step-by-step explanation:

y = 3x^2- 6x + 3

This has 1 real solutions.

y= -x^2 - 4x + 7

This has 2 real solutions.

y = -2x^2 + 9x – 11

This has 2 complex solutions.

${teks-lihat-gambar} caitlynm2395
boffeemadrid

The number of unique solutions each equation has is required.

[tex]y=3x^2-6x+3[/tex] has one real solution.

[tex]y=-x^2-4x+7[/tex] has two real solutions.

[tex]y=-2x^2+9x-11[/tex] has two complex solutions.

The number of solutions is determined by the value of the discriminant.

Let us find the determinant of each equation

[tex]y=3x^2-6x+3[/tex]

[tex]D=b^2-4ac\\\Rightarrow D=6^2-4\times 3\times 3\\\Rightarrow D=36-36\\\Rightarrow D=0[/tex]

The equation has one real solution.

[tex]y=-x^2-4x+7[/tex]

[tex]D=(-4)^2-4\times (-1)\times 7\\\Rightarrow D=16+28\\\Rightarrow D=44\\\Rightarrow D>0[/tex]

The equation has two real solutions.

[tex]y=-2x^2+9x-11[/tex]

[tex]D=9^2-4\times (-2)\times (-11)\\\Rightarrow D=81-88=-7\\\Rightarrow D<0[/tex]

The equation has two complex solutions.

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