Question

Y = – 2x² + 12x - 7

Answer 1

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:

 

a) What is equation of the axis of symmetry?

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.  

b) What is the vertex?

We can find the x-coordinate of the vertex by using the following formula:

$\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}$

Substitute the given values for a = -2, and b = 12 into the formula:

$\displaystyle\mathsf{x\:=\:\frac{-(12)}{2(-2)}\:=\:\frac{-12}{-4}\:=\:3}$

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).

c/d) Does the equation have a maximum or minimum? What is the maximum/minimum?

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.

• If a > 1, then it means that the graph of a parabola opens upward, and the vertex is its minimum point.

• If a < 0, then the graph of a parabola opens downward, and the vertex is its maximum point.  

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.