The vertex of the function is [tex]\boxed{\left( {0.5, - 0.75} \right)}[/tex] axis of symmetry is [tex]x = 0.5[/tex] and the formula for the function is [tex]\boxed{ - {x^2} + x - 1}.[/tex] Option (a) is correct.
Further Explanation:
Given:
Calculation:
The standard form of the parabola is shown below.
[tex]\boxed{y = a{{\left( {x - h} \right)}^2} + k}[/tex]
Here, the parabola has vertex at [tex]\left({h,k} \right)[/tex] and has the symmetry parallel to x-axis and it opens left.
The general form of the parabola can be expressed as follows,
[tex]y = a{x^2} + bx + c[/tex]
The graph is a downward parabola.
From the graph it has been observed that the vertex of the parabola is
[tex]\left( {0.5, - 0.75} \right).[/tex]
Symmetry of the graph is [tex]x = 0.5.[/tex]
The [tex]y[/tex]-intercepts of the graph is [tex]-1.[/tex] Therefore, the value of [tex]c[/tex]is [tex]-1.[/tex]
The value of [tex]a[/tex] is -1 as the graph is a downward parabola.
The vertex of the function is [tex]\boxed{\left( {0.5, - 0.75} \right)}[/tex] axis of symmetry is [tex]x = 0.5[/tex] and the formula for the function is [tex]\boxed{ - {x^2} + x - 1}.[/tex] Option (a) is correct.
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear [tex]x = 0.5.[/tex]https://brainly.com/question/4165000
3. Learn more aboutbinomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Conic sections
Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola.
