Question

I did something wrong here according to my teacher. Can you help?

Answer 1

• Line of Symmetry: x=-0.5

,

• Vertex: (-0.5, 5.5)

,

• Maximum

,

• y-intercept: (0, 3)

Explanation:

Given the quadratic function:

`y=-10x^2-10x+3`

Comparing with the form y=ax²+bx+c:

`a=-10,b=-10,c=3`

(a)Line of Symmetry

The equation of symmetry is determined using the formula:

`\begin{gathered} x=-(b)/(2a) \\ =(-(-10))/(2(-10)) \\ =(10)/(-20) \\ x=-0.5 \end{gathered}`

(b)Next, we find the corresponding y-value.

`\begin{gathered} y=-10x^(2)-10x+3 \\ y=-10(-0.5)^2-10(-0.5)+3 \\ y=5.5 \end{gathered}`

The vertex of the parabola is (-0.5, 5.5).

(c)Since the value of a is negative, the vertex is a maximum.

(d)y-intercept

The y-intercept is the value of y when x=0.

`\begin{gathered} y=-10x^(2)-10x+3 \\ y=-10(0)^2-10(0)+3 \\ y=3 \end{gathered}`

The y-intercept is at (0, 3).