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I need help with this question please. (It’s also just a homework practice).

I need help with this question please. (It’s also just a homework practice).-example-1
User ColinTea
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1 Answer

28 votes
28 votes

We need to graph the next function:


y=x^2-6x-4

This is a parabola, and we need 3 points to graph it.

The x-coordinate of a parabola is computed as follows:


x_V=(-b)/(2a)

where a and b are the coefficients of the parabola. Substituting with a = 1, and b = -6, we get:


\begin{gathered} x_V=(-(-6))/(2\cdot1) \\ x_V=3 \end{gathered}

The y-coordinate of the vertex is found substituting xV into the equation as follows:


\begin{gathered} y_V=x^2_V-6x_V-4 \\ y_V=3^2-6\cdot3-4 \\ y_V=9-18-4 \\ y_V=-13 \end{gathered}

The vertex is the point (3, -13)

Substituting x = 2 into the equation of the parabola, we get:


\begin{gathered} y=2^2-6\cdot2-4 \\ y=4-12-4 \\ y=-12 \end{gathered}

Substituting x = 4 into the equation of the parabola, we get:


\begin{gathered} y=4^2-6\cdot4-4 \\ y=16-24-4 \\ y=-12 \end{gathered}

Then, the parabola passes through the points (2, -12) and (4, -12). Connecting these points and the vertex, we get the next graph:

The line y = 3 is shown in green.

From the graph, we can see that the parabola (x²-6x-4, in blue) is greater than 3 (in green) for the next values of x:

x < -1 or x > 7

I need help with this question please. (It’s also just a homework practice).-example-1
User Naveen Kumar H S
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3.0k points