1.) If a = 2 and the vertex of a parabola is (3, -4), will there be a minimum or maximum value for the parabola? What is the value?
2.) If a = 2 and the vertex of a parabola is (3, -4), what is its axis of symmetry?
To determine the minimum or maximum value of a parabola with a given vertex, we need to understand the properties of the parabola and its equation.
1.) If a = 2 and the vertex of a parabola is (3, -4), there will be a minimum value for the parabola. The vertex form of a parabola's equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, h = 3 and k = -4.
To find the minimum value, we need to substitute the values of h and k into the equation. Thus, the equation becomes y = 2(x - 3)^2 - 4.
For this equation, the coefficient "a" is positive (a = 2), which means the parabola opens upwards, indicating a minimum value. The value of the minimum point can be found by evaluating the y-coordinate of the vertex. In this case, the minimum value is -4.
2.) To determine the axis of symmetry of a parabola, we can extract the value of "h" from the vertex. In this case, the vertex is given as (3, -4), which means h = 3.
The axis of symmetry of a parabola is a vertical line that passes through its vertex. Since the vertex has an x-coordinate of 3, the equation of the axis of symmetry is x = 3.
1.
equation will be y = 2(x-3)^2 - 4
since the parabola opens upwards, there will be a minimum
That minimum is -4 and it occurs when x = 3
2. same equation
if your equation is y = a(x-p)^2 + q
the vertex is (p,q)
it will open up if a>0
it will open down if a< 0
the axis of symmetry will be x-p=0 or x = p
the max/min will be q , when x = p