Question

Select the statements that are true for the graph of y=(x−1)2−6

The vertex is (1, -6)
The vertex is (2, 4)
The graph has a minimum
The graph has a maximum

Answer 1

The two statements that are true is that the graph has a minimum and the vertex is (1, -6).

To find if a graph has a minimum or a maximum, it is very simply. We look for the lead coefficient of x^2 or in vertex form (which it is currently in), the number in front of the parenthesis. In this case, we don't see one, so we assume it is 1. If this number is positive, it means the graph has a minimum. If the graph has a negative, it means there is a maximum.

As for the vertex, we first must know the standard vertex form seen below.

y = a(x - h)^2 + k

In this equation, a is the constant and (h, k) is the vertex. If we look at the equation where it is, we can locate the h and k without doing any mathematical work.

y = (x - 1)^2 - 6

h k

So we know our vertex must be those numbers (1, -6)

Answer 2

By analyzing the quadratic function, we will see that:

• The vertex is (1, -6)
• The graph has a minimum.

What statements are true about the graph?

Here we have the quadratic function written in vertex form:

y = (x - 1)^2 - 6

Remember that when the vertex is (h, k), the vertex form is:

y = a*(x - h)^2 + k.

So here we can see that the vertex is (1, -6), meaning that the first option is correct.

Also, we have a positive leading coefficient (1, the value that multiplies the parenthesis). That means that the arms of the graph open upwards, so there is no maximum, but there is a minimum at the vertex.

In this case, the minimum is y = -6.

Concluding, the correct options are:

• The vertex is (1, -6)
• The graph has a minimum.

If you want to learn more about quadratic equations, you can read:

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