Question

Complete the square of the function y = −5x2 + 10x + 12.

Part A: Where is the vertex located and what is the maximum or minimum value? What is the equation of the axis of symmetry?

Part B: What are the zeros of the function (as exact values expressed in radical form) and the y-intercept?

Answer 1

@carlyleukhardt please help

Answer 2

can u use completing the square?

Answer 3

its simply taking 10x dividing it by 2 squaring it adding and subtracting your answers and then factor

Answer 4

I dont understand how to do any of it

Answer 5

Ok lets start on the first step of completing the square. You have the equation.

\[5x ^{2}+10x + 12\]

Answer 6

5x2+10x+12 = 0

Answer 7

Now subtract the number on both sides of the equation for the one that does not have an X multiplying it

Answer 8

What do you get?

Answer 9

5x^2-10x=-12? that doesn't sound right

Answer 10

don't complete the square like that

factor out the -5

so its

\[-5(x^2 - 2x + ?)\]

a perfect square is in the form

\[x^2 + bx + c~~~~~Where~~~ c = (\frac{b}{2})^2\]

so what is half of -2 then square that value... that's what you need to add

Answer 11

-1 is half of -2 then -1 squared is i right?

Answer 12

Find what c equals in the equation where
a=5
b=2
and c=?

when you factor out negative 5 from the equation

\[a(x ^{2}+bx+c) || c=\left( \frac{ b }{ 2 } \right)^{2}\]

Answer 13

So plug b into the second equation

Answer 14

What do you get

Answer 15

Actually a=-5

Answer 16

well if you square -1 its -1 x -1 = ?

Answer 17

1

Answer 18

ok... so its now

\[y = -5(x^2 -2x + 1) + 12\]

so now you need to add the opposite value so add 5

and you get

\[y = -5(x^2 -2x +1) + 17\]

now just factor the perfect square and the vertex form of the parabola is

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

where (h, k) is the vertex

Answer 19

in your question the value of a is -5

so factor your equation so it matches the standard form