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I need help with this quadratic function… I thought I knew the answer, but obviously I don’t

I need help with this quadratic function… I thought I knew the answer, but obviously-example-1
User LvN
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Let us start with the following quadratic function:


f(x)=x^2-x-12

the X-intercepts are the collection of values to X which makes f(x) = 0, and it can be calculated by the Bhaskara formula:


x_(1,2)=(-b\pm√(b^2-4ac))/(2a)

where the values a, b, and c are given by:


f(x)=ax^2+bx+c

Substituting the values from the proposed equation, we have:


\begin{gathered} x_(1,2)=(1\pm√(1^2-4*1*(-12)))/(2*1) \\ x_(1,2)=(1\pm√(1+48))/(2)=(1\pm√(49))/(2) \\ x_(1,2)=(1\pm7)/(2) \\ \\ x_1=(1+7)/(2)=(8)/(2)=4 \\ x_2=(1-7)/(2)=-(6)/(2)=-3 \end{gathered}

From the above-developed solution, we are able to conclude that the solution for the first box is:

(-3,0) ,(4,0)

Now, the y-intercept, is just the value of y when x = 0, which can be calculated as follows:


\begin{gathered} f(0)=0^2-0-12=-12 \\ f(0)=-12 \end{gathered}

From this, we are able to conclude that the solution for the second box is:

(0, -12)

Now, the vertex is the value of minimum, or maximum, in the quadratic equation, and use to be calculated as follows:


\begin{gathered} Vertex \\ x=-(b)/(2a) \\ y=(4ac-b^2)/(2a) \end{gathered}

substituting the values, we have:


\begin{gathered} x=-(-1)/(2*1)=(1)/(2) \\ y=(4*1*(-12)-(-1)^2)/(4*1)=(-48-1)/(4)=(-49)/(4) \end{gathered}

which means that the solution for the thirst box is:

(1/2, -49/4) (just as in the photo)

Now, the line of symmetry equation of a quadratic function is a vertical line that passes through the vertex, which was calculated to be in the point: (1/2, -49,4).

Because this is a vertical line, it is represented as follows:


x=(1)/(2)

User Teocomi
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