Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.

a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.

When a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards and from the given equation a < 0 that is why the graph of the quadratic equation is a parabola that opens downward.

Given :

Quadratic Function --- [tex]y = -x^2-10x + 1[/tex]

The graph of the quadratic equation is in the shape of the parabola. The generalized quadratic equation is given by:

[tex]ax^2 + bx +c = 0[/tex]

Now, compare the given equation ([tex]y = -x^2-10x + 1[/tex]) with the generalized quadratic equation which is given above.

[tex]a = -2[/tex]

b = -10

c = 1

According to the rules of the graph, when a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards.

Therefore, the correct option is c).

For more information, refer to the link given below:

https://brainly.com/question/17267403

Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain. a. Because a > 0, the parabola opens downward. b. Because a < 0, the parabola opens upward. c. Because a < 0, the parabola opens downward. d. Because a > 0, the parabola opens upward.

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Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.

a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.