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Find the x-intercepts for the parabola defined
by this equation:
y = 2x² – 12x + 10
Write your answer as two ordered pairs:
(x1, y1), (x2, y2)
Separate the values with a comma. Round, if
necessary, to the nearest hundredth.

Respuesta :

danielmaduroh

Answer:

Explanation:

In this exercise we have the following equation of a parabola:

[tex]y=2x^2-12x+10[/tex]

So our goal is to find the x-intercepts. We can find this setting [tex]y=0[/tex], so:

[tex]2x^2-12x+10=0[/tex]

Taking 2 as common factor:

[tex]2(x^2-6x+5)=0[/tex]

Hence this is a Non-perfect Square Trinomial. To factor out this, let's choose two numbers such that:

  • The sum is -6
  • The product is 5

Those two numbers are:

  • -1 and -5

Because:

  • Sum: -6
  • Product: 5

So this equation can be written as:

[tex]x^2 + (a + b)x + ab=(x + a)(x + b) \\ \\ a=-1 \\ b=-5 \\ \\  x^2-14x+24=(x-(-1))(x-(-5))=0 \\ \\ (x+1)(x+5)=0 \\ \\ So \ the \ solutions \ are: \\ \\ \boxed{x=-1 \ and \ x=-5}[/tex]

Learn more:

Solutions to quadratic equation: https://brainly.com/question/13742278#

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