Answer:
• Line of Symmetry: x=-0.5
,
• Vertex: (-0.5, 5.5)
,
• Maximum
,
• y-intercept: (0, 3)
Explanation:
Given the quadratic function:
[tex]y=-10x^2-10x+3[/tex]
Comparing with the form y=ax²+bx+c:
[tex]a=-10,b=-10,c=3[/tex]
(a)Line of Symmetry
The equation of symmetry is determined using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =\frac{-(-10)}{2(-10)} \\ =\frac{10}{-20} \\ x=-0.5 \end{gathered}[/tex]
(b)Next, we find the corresponding y-value.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(-0.5)^2-10(-0.5)+3 \\ y=5.5 \end{gathered}[/tex]
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.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(0)^2-10(0)+3 \\ y=3 \end{gathered}[/tex]
The y-intercept is at (0, 3).
