Using the given quadratic function, it is found that:
a) The vertex is (-2.5, -15.5).
b) The y-intercept is of -3.
c) The solutions are x = -0.28, x = 5.28.
What is the quadratic function?
It is modeled by:
f(x) = 2x² - 10x - 3.
Which means that the coefficients are a = 2, b = -10, c = -3.
What is the vertex of the function?
It 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]
Hence:
[tex]x_v = -\frac{-10}{4} = -2.5[/tex]
[tex]y_v = -\frac{(-10)^2 - 4(2)(-3)}{8} = -15.5[/tex]
The vertex is (-2.5, -15.5).
What is the y-intercept of the equation?
It is the value of coefficient c, hence it is of -3.
What are the solutions?
[tex]\Delta = b^2 - 4ac = (-10)^2 - 4(2)(-3) = 124[/tex]
[tex]x_1 = \frac{10 + \sqrt{124}}{4} = 5.28[/tex]
[tex]x_2 = \frac{10 - \sqrt{124}}{4} = -0.28[/tex]
The solutions are x = -0.28, x = 5.28.
More can be learned about quadratic functions at https://brainly.com/question/24737967
