Mathematics, 06.10.2019 19:00 Sqeauky

Without drawing the graph of the equation answer the question. how many points does the given equation have in common with the x-axis and where is the vertex in relation to the x-axis? y=x^2-12x+12

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Answer from: quoia89

There are two points common with the x-axis

The vertex is under the x-axis by 24 units at x = 6

Step-by-step explanation:

* For the quadratic equation y = ax² + bx + c

- The roots of the equation are the intersection point between

the equation and the x-axis ⇒ y = 0

- To find these roots we factorize the equation into two factors

and equate each factor with zero

- The graph of the quadratic equation is called parabola,

the parabola has vertex point. If the vertex point is (h , k)

∴ h = -b/2a, where b is the coefficient of x and is the coefficient of x²

∴ k = y where x = h

* Lets solve the problem

∵ y = x² - 12x + 12

- The formula to find the values of x when y = 0 is

$x=\frac{-b+\sqrt{b^{2}-4ac}}{2a},x=\frac{-b-\sqrt{b^{2}-4ac}}{2a}$

∵ a = 1 , b = -12 , c = 12

∴ $x=\frac{-(-12)+\sqrt{(-12)^{2}-4(1)(12)}}{2(1)}=\frac{12+\sqrt{144-48}}{2}$

∴ $x=\frac{12+\sqrt{96}}{2}=\frac{12+4\sqrt{6}}{2}=6+2\sqrt{6}$

∴ The two roots are 6 + 2√6 and 6 - 2√6

* There are two points common with the x-axis

* Lets calculate the vertex

∵ h = -b/2a

∵ b = -12 and a = 1

∴ h =-(-12)/2(1) = 12/2 = 6

∴ k = (6²) - 12(6) + 12 = 36 - 72 + 12 = -24

∴ The vertex is (6 , -24)

* That means the vertex is under the x-axis by 24 units at x = 6

Answer from: Quest

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves

What is the slope of a line that is parallel to the line shown? taking quiz need

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc