Question

The equation f(x) = 5x2 − 30x + 6 represents a parabola. What is the vertex of the parabola?

(−5, 281)
(5, −19)
(−3, 141)
(3, −39)

Answer 1

In the general equation of a parabola\[f \left( x \right) = ax ^{2} + bx + c\]The x-coordinate of the vertex is given by\[x=-\frac{ b }{ 2a }\]Then calculate f(x) using this value of x to give you the y-coordinate of the vertex.

Answer 2

Would it be B?

Answer 3

Don't think so.

Answer 4

Sorry trying to figure this out haha math isn't my best subject so its a little harder let me try to recalculate

Answer 5

No problem. Take your time. What do you get for the x-coordinate? (-b/2a)

Answer 6

would the x coordinate be -39/2a?

Answer 7

Not quite. From looking at the given quadratic, what is the value of a and the value of b?

Answer 8

a multiplies x^2 and b multiplies the x

Answer 9

honestly I have no clue I'm so confused on how to do this could you explain like in details like how to solve it

Answer 10

I just did. But let's back up. The given quadratic function is\[f \left( x \right) = 5x ^{2} - 30x + 6\]Compare that with\[f \left( x \right) = ax ^{2} + bx + c\]a is the number that multiplies x^2
b is the number that multiplies x
What are they?

Answer 11

a is 5 and b is -30??

Answer 12

Perfect. Now the x-coordinate is given by\[x = -\frac{ b }{ a }\]Plug in those values of a and b . What do you get?

Answer 13

Sorry. It's\[x=-\frac{ b }{ 2a }\]

Answer 14

So you're calculating\[x=-\frac{ b }{ 2a } = -\frac{ -30 }{ 2\left( 5 \right) } = ?\]

Answer 15

-75?

Answer 16

Nope. What is 2 x 5 ?

Answer 17

10

Answer 18

Good. That's the denominator. Now, what's -30/10 ?

Answer 19

-3

Answer 20

Good. Finally, what's -(-3) ?

Answer 21

3

Answer 22

Excellent. So the x-coordinate of the vertex is 3.

Answer 23

Now, to get the y-coordinate of the vertex, put his value of x into the original function and calculate f(3)\[f \left( x \right)=5x ^{2}-30x+6\]\[f \left( 3 \right) = 5\left( 3 \right)^{2}-30\left( 3 \right) + 6\]What do you get?

Answer 24

-18?

Answer 25

Nope. What is 3^2 ?

Answer 26

9

Answer 27

Great. Now what is 5 x 3^2 ?

Answer 28

45

Answer 29

Good. Now what is 30 x 3 ?

Answer 30

90

Answer 31

Great. Now to put it all together\[f \left( 3 \right) = 5\left( 3 \right)^{2} - 30\left( 3 \right) + 6 = 45-90+6 = ?\]

Answer 32

-39

Answer 33

Good. Now you have the x- and y-coordinates of the vertex. Where is the vertex?

Answer 34

3,-39 is my answer?

Answer 35

That's it. Well done.

Answer 36

thank you so much for being patient with me! and helping me understand!

Answer 37

You're welcome. Good luck with your studies.