Question

F(x) =x^2-3x-18 vertex?

Answer 1

• (3/2, -81/4)

Explanation:

Rewrite in vertex form and use this form to find the vertex (h, k).

Answer 2

`\sf Vertex \left((3)/(2), (-81)/(4)\right)`

Explanation:

Vertex of quadratic function:

• Write the equation in vertex form by using the method completing the square.

y = x² - 3x - 18

Add 18 to both sides.

y + 18 = x² - 3x

Divide the co-efficient of x by 2 and square the result and then add it to both sides.

Co-efficient of x = 3. Divide 3 by 2and add (3/2)² to both sides

`\sf y + 18 + \left((3)/(2)\right)^2= x^2 - 3x + \left((3)/(2)\right)^2\\\\\\y + 18+(9)/(4)=x^2 - 3x + (9)/(4)\\\\\\`

`\sf y + (18*4)/(1*4)+(9)/(4)=\left(x - (3)/(2)\right)^2\\\\\\y + (72)/(4)+(9)/(4)=\left(x - (3)/(2)\right)^2\\\\\\y + (81)/(4)=\left(x-(3)/(2)\right)^2\\\\ y = \left(x-(3)/(2)\right)^2 -(81)/(4)\\\\`

Vertex form: f(x) = (x - h)² + k

where h and k are the vertex co-ordinates.

`\sf \boxed{\bf Vertex \left((3)/(2), (-81)/(4)\right)}`