Answer:
a) axis of symmetry: x = h
b) Vertex: (3, 11).
c/d) Maximum point = vertex (3, 11).
Step-by-step explanation:
Note: This post will only provide the answers for parts a through d, in accordance with Brainly's Guidelines.
Given the quadratic equation, y = – 2x² + 12x - 7, where a = -2, b = 12, and c = -7:
The axis of symmetry is an imaginary line that divides the graph of a parabola into two symmetrical parts. The axis of symmetry goes through the x-coordinate of the vertex, (h, k). Hence, the axis of symmetry is often represented by the following equation: x = h.
We can find the x-coordinate of the vertex by using the following formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}[/tex]
Substitute the given values for a = -2, and b = 12 into the formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-(12)}{2(-2)}\:=\:\frac{-12}{-4}\:=\:3}[/tex]
Hence, the x-coordinate of the vertex is 3.
Substitute x = 3 into the given quadratic equation to find its corresponding y-coordinate:
y = – 2x² + 12x – 7
y = – 2(3)² + 12(3) – 7
y = –2(9) + 36 – 7
y = – 18 + 36 – 7
y = 11
Therefore, the vertex of the given quadratic equation is (3, 11).
The value of the "a" coefficient in the quadratic equation, y = ax² + bx + c, determines whether a given parabola has either a minimum, or a maximum.
Since the value of our given quadratic equation is a = -2, then it means that its graph opens downward, and that the vertex is its maximum point.
Attached is a screenshot of the graph, where it shows the vertex occurring at point (3, 11), for which the axis of symmetry goes through at x = 3.
