Question

1. Find the vertex of the following: y = (x - 4)(x - 10) *

(7, -9)
(3, -9)
(4, 10)
2. Find the intercepts of the following: y = (x - 4)(x - 10) *
(4, 0) and (10,0)
(0, 4) and (0, 10)
3 Find the intercepts of the following: y = (x - 3)(x + 3) *
(3, 0) and (-3,0)
(0, 3) and (0, -3)
4 Find the vertex of the following: y = (x - 3)(x + 3) *
(0, -9)
(0, -6)
(3, -3)
5. Find the vertex of the following: y = 2(x - 3)(x + 5) *
(-16, -32)
(-8, 2)
(-1, -32)

PLEASE HELP ME!!!!

Answer 1

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Explanation:

To find the vertex use the formula

`(-b)/(2a)`

First make the equation into a quadratic equation.

`(x-4)(x-10)\\x^(2) -10x-4x+40\\x^(2) -14x+40`

Now it is in the form

`ax^(2) +bx+c=0`

Now we can substitute the values

`(-(-14))/(2(1)) \\(14)/(2) \\7`

Now we have 7 as our x value for the vertex we can substitute for y,

`x^(2) -14x+40=y\\(7)^(2) -14(7)+40=y\\49-98+4=y\\y=-9`

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

`x-4=0\\x=4\\\\x-10=0\\x=10`

4 is slightly different but start the same,

`(x-3)(x+3)\\x^(2)+3x-3x-9\\x^(2)-9`

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

`2(x-3)(x+5)\\2(x^(2)+5x-3x-15)\\2(x^(2)+2x-15)\\2x^(2)+4x-30`

Vertex,

`(-(4))/(2(2)) \\(-4)/(4) \\-1`

Substitute,

`2x^(2)+4x-30\\2(-1)^(2)+4(-1)-30\\2-4-30\\-32`

So the vertex is (-1,-32)