Question

Could you please help me with these problems?

[9.01] Determine whether the graph of y = −3x2 + 2x − 8 opens up or down and whether it has a maximum or minimum point.
Up; Minimum
Up; Maximum
Down; Minimum
Down; Maximum

[9.01] Determine whether the graph of y = x2 + 4x − 7 has a maximum or minimum point, then find the maximum or minimum value.
Minimum; (-11, -2)
Maximum; (-11, -2)
Maximum; (-2, -11)
Minimum; (-2, -11)

[9.02] What are the x-intercept(s) of the graph of y + 20 = x2 − x?
(−5, 0) and (4, 0)
(5, 0) and (−4, 0)
(−5, 0) and (−4, 0)
(5, 0) and (4

Answer 1

\[y = −3x^2 + 2x − 8 \] the leading coefficient is negative (it is \(-3\)) so it opens down

Answer 2

since it opens down it has a max, but no minimum

Answer 3

\[y = x^2 + 4x − 7\] positive leading coefficient, it is 1, so it opens up
therefore it has a min, not max
minimum is at the second coordinate of the vertex
first coordinate of the vertex is always \(-\frac{b}{2a}\) which in your case is \(-\frac{4}{2}=-2\)
second coordinate is what you get when you replace \(x\) by \(-2\)

Answer 4

Thanks so much. Now I just have to try to figure out the other one. :/