Question

What is the vertex of y = −3x2 + 6x + 17

Answer 1

vertex = ( 1, 30 )

Explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 ) , then

the x-coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

given

y = - 3x² + 6x + 17 ← in standard form

with a = - 3 and b = 6 , then

`x_(vertex)` = -
`(6)/(2(-3))` = -
`(6)/(-6)` = - (- 1) = 1

substitute x = 1 into y for corresponding y- coordinate

y = - 3(1)² + 16(1) + 17

= - 3(1) + 16 + 17

= - 3 + 33

= 30

vertex = (1, 30 )

Answer 2

Explanation:

I can help you find the vertex of that quadratic function, but first let's review the vertex form of a parabola. A parabola's vertex is given by the formula (h, k), where h and k are the x and y values, respectively, of the vertex. Now let's write the given equation in vertex form. To do this, we'll factor out -3 and complete the square. Here's the process:

y = -3x2 + 6x + 17

y = -3(x2 + 2x) + 17

y = -3(x2 + 2)

Now that we've put the equation in vertex form, we can see that h = -2 and k = 17. So, the vertex is (-2, 17). That means the x-coordinate of the vertex is -2, and the y-coordinate is 17.