Finding the vertex of the quadratic functions, the correct statement is:
Function 1 has the larger maximum at (4, 1).
What is the vertex of a quadratic equation?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
- [tex]x_v = -\frac{b}{2a}[/tex]
- [tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
For function 1, we have that:
f(x) = -x² + 8x - 15.
Hence the coefficients are a = -1, b = 8, c = -15, and the vertex is:
- [tex]x_v = -\frac{8}{2(-1)} = 4[/tex]
- [tex]y_v = -\frac{8^2 - 4(-1)(-15)}{4(-1)} = 1[/tex]
For function 2, we have that:
f(x) = -x² + 2x - 3.
Hence the coefficients are a = -1, b = 2, c = -3, and the vertex is:
- [tex]x_v = -\frac{2}{2(-1)} = 1[/tex]
- [tex]y_v = -\frac{2^2 - 4(-1)(-3)}{4(-1)} = -2[/tex]
1 > -2, hence the correct statement is:
Function 1 has the larger maximum at (4, 1).
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
#SPJ1
