Question

Find the x-intercepts for the parabola defined

Answer 1

Answer:

Explanation:

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

$y=2x^2-12x+10$

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

$2x^2-12x+10=0$

Taking 2 as common factor:

$2(x^2-6x+5)=0$

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:

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

Learn more:

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

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