Mathematics: What are the vertex and x-intercepts of the graph of y=x^2-2x-24

Не говорю по английски Step-by-step explanation:...

What are the vertex and x-intercepts of the graph

RebelZane18

16.01.2022

Vertex : (1,-25) ; x intercepts : (6,0)&(-4,0)

Step-by-step explanation:

$y=x^{2}-2x-24$

adding 25 on both sides

$y+25=x^{2}-2x-24+25$

$y+25=x^{2}-2x+1$

$y+25=x^{2}-2*1*1*x+1^{2}$

$y+25=(x-1)^{2}$

let us convert the above equation in the standard form

let y+25=Y

x-1=X

$X^{2}=4*\frac{1}{4}*Y$

vertex of above equation is (0,0)

replacing them into original form is x-1=0 , x=1

y+25=0 ; y=-25

Hence the vertex is (1,-25)

Part 2 :

In order to find the x intercepts , we put y=0 and solve for x

$0+25=(x-1)^{2}$

$25=(x-1)^{2}$

taking square roots on both sides we get

±5=x-1

solving get x=±5+1 ; x=5+1=6 ; x=-5+1=-4

Hence y intercepts are (-4,0) & (6,0)

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