Question

Graph the function then find the zeros for the function
Y=x² + 6x + 8
Axis of symmetry
Vetex
Y-intercept
Other point
zeros

Answer 1

To graph the function y = x^2 + 6x + 8, we first need to find the axis of symmetry, vertex, y-intercept, and zeros.

Axis of symmetry:
The axis of symmetry for a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a). In this case, a = 1 and b = 6. Plugging these values into the formula gives x = -6/(2*1) = -3. Therefore, the axis of symmetry for this function is x = -3.

Vertex:
To find the vertex, we substitute the x-coordinate of the axis of symmetry into the function. y(-3) = (-3)^2 + 6(-3) + 8 = 9 - 18 + 8 = -1. Therefore, the vertex is (-3, -1).

Y-intercept:
To find the y-intercept, substitute x = 0 into the function. y(0) = (0)^2 + 6(0) + 8 = 8. Therefore, the y-intercept is (0, 8).

Other point:
Let's find a point on the graph that is not the vertex or the y-intercept. For example, when x = 1, y = 1^2 + 6(1) + 8 = 1 + 6 + 8 = 15. Therefore, the point (1, 15) is also on the graph.

Zeros:
To find the zeros of the function, we set y = 0 and solve for x. x^2 + 6x + 8 = 0 can be factored into (x + 2)(x + 4) = 0. Setting each factor to zero gives x = -2 or x = -4. Therefore, the zeros of the function are -2 and -4.

Now, we can graph the function y = x^2 + 6x + 8. The graph will have a parabolic shape opening upwards with the vertex at (-3, -1), y-intercept at (0, 8), point (1, 15), and the zeros at x = -2 and x = -4.