Question

Find the maximum or minimum of the following quadratic function: y =x2 - 2x - 48.
A. -49
B. 49
C. 48
D. -48

Answer 1

To find the minimum or maxium, you need to take the first derivative of the given function.

Answer 2

i dont get it

Answer 3

Do you know how to take derivatives?

Answer 4

@miryluslinares are you doing calc?

Answer 5

no i am doing algebra 2

Answer 6

If this is not for calculus, you need to put it in standard form: y=A(x-h)\(^2\)+k,
where (h,k)=(x,y) are the coordinates of the vertex

Answer 7

That means, completing the square.

Answer 8

I assume you've done parabolas, so, the minimum or maximum, will be at the LOWEST or HIGHEST point of the parabola, and that occurs at its vertex

you can find the vertex of a parabola \(\bf ax^2+bx+c\) at \(\bf \left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\)

Answer 9

or you can also as abb0t said, complete the square and get the "vertex form" of the parabola, that'd work too

Answer 10

keep in mind that, what they mean by "minimum" or "maximum", is just the "hump" the parabola has, which is also the "vertex"

Answer 11

how would i plug it in that that equation its because i am taking an online class and i am lost

Answer 12

\(\large \begin{array}{lllllll}
&a&&b&&c\\
y =x^2 - 2x - 48 \implies y =&1&x^2 &- 2&x &- 48

\end{array}\\\quad \\
\bf \left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\)


notice the coefficients

Answer 13

ohhh ok i get it thank you very much :)

Answer 14

yw

Answer 15

@jdoe0001 so its D right?

Answer 16

well, they're asking for the value for "y", that is, f(x) at the vertex, so, they want the y-coordinate of it

\(\bf \large \qquad x \qquad \qquad y\\
\left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\)

Answer 17

so, what did you get for "y"?

Answer 18

i got -48.5

Answer 19

am i doing it right?

Answer 20

let's see

\(\large \begin{array}{lllllll}
&a&&b&&c\\
y =x^2 - 2x - 48 \implies y =&1&x^2 &- 2&x &- 48

\end{array}\\\quad \\
\bf \left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\\ \quad \\
c-\cfrac{b^2}{4a} \implies (-48)-\cfrac{(-2)^2}{4(1)}\)

Answer 21

nevermind i got -49 thank you for taking the time to help me

Answer 22

yw