The coordinate of the vertex is [tex]\boxed{(2,-10)}[/tex] and the axis of symmetry is [tex]\boxed{x=2}[/tex].
Further Explanation:
The general form of a quadratic equation is as follows:
[tex]\boxed{y=ax^{2}+bx+c}[/tex] ……(1)
To find the vertex of the quadratic equation [tex]y=ax^{2}+bx+c[/tex], we have to calculate [tex]-\frac{b}{2a}[/tex] which is the [tex]x[/tex] coordinate of the vertex.
Then Substitute value of [tex]x[/tex] in the given quadratic equation to obtain [tex]y[/tex] coordinates of the vertex.
The axis of symmetry of a parabola is a vertical line which divides the parabola into two equal halves and the axis of symmetry always passes through the vertex of parabola.
The coordinate of the vertex is the equation of the axis of symmetry of the parabola which means [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry.
The given equation is [tex]y=-2x^{2}+8x-18[/tex] and the value of [tex]a[/tex] is [tex]-2[/tex], [tex]b[/tex] is [tex]8[/tex] and [tex]c[/tex] is [tex]-18[/tex] from the given equation.
The [tex]x[/tex] coordinates of the vertex is calculated as follows:
[tex]\begin{aligned}x&=-\dfrac{b}{2a}\\&=\dfrac{-8}{2\cdot (-2)}\\&=2\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]\bf 2[/tex].
Then substitute the value of [tex]x[/tex] in equation (1) to obtain the value of [tex]y[/tex]-coordinate of the vertex.
[tex]\begin{aligned}y&=-2\cdot (2)^{2}+(8\cdot 2)-18\\&=-8+16-18\\&=8-18\\&=-10\end{aligned}[/tex]
Therefore, the the value of [tex]y[/tex] is [tex]\bf -10[/tex].
So, the coordinates of the vertex of the equation [tex]y=-2x^{2}+8x-18[/tex] is [tex](2,-10)[/tex].
The axis of symmetry is [tex]x=2[/tex].
Thus, the coordinate of the vertex is [tex]\boxed{(2,-10)}[/tex] and the axis of symmetry is [tex]\boxed{x=2}[/tex].
Learn more:
1. Learn more about the axis of symmetry for a function https://brainly.com/question/1286775
2. Learn more about the y-intercept of the quadratic function https://brainly.com/question/1332667
3. Learn more about has the equation of a line https://brainly.com/question/1473992
Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Conic section
Keywords: Axis, coordinate points, axis of symmetry, quadratic equation, vertex, y=-2x2+8x-18, parabola, x coordinates, y coordinates, symmetry, degree, highest power, curve, axis of symmetry.
