Answer:
The solution set is ∅
Step-by-step explanation:
The expression
y = ax^2 + bx + c
is a quadratic equation.
The vertex is located at (-2, 5) and the graph opens up, this means that it never intercepts the x-axis.
The solution set is ∅
Please see attached image
Answer:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Step-by-step explanation:
Assume c = 0
Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:
[tex]x=\frac{-b}{2a} \\-2=\frac{-b}{2a} \\b=4a[/tex]
B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:
[tex]y=ax^{2}+bx\\y=ax^{2}+4ax\\5=a(-2)^{2}+4(-2)a\\5=4a-8a\\5=-4a\\a=\frac{5}{-4}[/tex]
AND
[tex]b=4a\\b=\frac{-5}{4} *4\\b=-5[/tex]
Substituting into the quadratic equation:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Because a is negative, the parabola opens up.
