Find the vertex of the graph of the equation. y=x^{2}-x-3 (x,y)=()

Cordazzoyn

Cordazzoyn

Answered question

2021-11-18

Find the vertex of the graph of the equation.
y=x2x3
(x,y)=()

Answer & Explanation

Gloria Lusk

Gloria Lusk

Beginner2021-11-19Added 18 answers

Step 1
Given data:
The quadratic equation is:
y=x2x3...(1)
To determine the vertex of the graph of the above equation (1), that is, to compute the x and y co-ordinates.
Step 2
The graph of any quadratic equation is a parabola.
Comparing equation (1) to the standard form of quadratic equation ax2+bx+c, following values are obtained as:
a=1
b=-1
c=-3
Computing the axis of symmetry, an imaginary line that divides the parabola into two equal halves, as:
x=b2a
=(1)2×1
=12
=0.5
So, the x-value of the vertex of the graph of the given equation is 0.5.
From equation (1), solving for y with the value of x = 0.5,
y=(0.5)20.53
=0.25-0.5-3
=-3.25
So, the y-ordinate of the vertex of the graph of the given equation is -3.25.
Therefore, the vertex of the graph of the given equation is:
(x, y)=(0.5,−3.25)
Steacensen69

Steacensen69

Beginner2021-11-20Added 15 answers

y=x2x3
It is an Quadratic function, of the form Ax2+bx+c, whose Graph is a Parabola & Vertex (b2a,D4a)
y=x2x3
here a=1, b=-1. c=-3
[Discriminant (D)=b24ac]
D=(1)241(3)
=1+12=13
So,
x-Coordinate =b2a=(1)21
=12.
y-Coordinate =D4a=134
So Vertex =(12,134)

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