We will start by identifying the values of a, b, and c.
f(x)=- 1x^2+10x-13 ⇕ f(x)=(-1)x^2+ 10x+( - 13)We can see that a = - 1, b = 10, and c = - 13. Since the y-intercept is given by the value of c, we know that the y-intercept is - 13. Let's now substitute a=- 1 and b=10 into - b2a to find the axis of symmetry.
The equation of the axis of symmetry is x=5.
To find the vertex of the parabola, we will need to think of y as a function of x, y=f(x). We can write the expression for the vertex by stating the x- and y-coordinates in terms of a and b.
Vertex: ( - b/2a, f(- b/2a ) )
When determining the axis of symmetry, we found that - b2a=5. Therefore, the x-coordinate of the vertex is 5 and the y-coordinate is f(5). To find this value, substitute our x-coordinate for x in the given equation.
