Can you please help me with the following problems?
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
1.f(x) = (x - 4)2 - 4
Find the axis of symmetry of the parabola defined by the given quadratic function.
3.f(x) = (x + 2)2 + 7
Find the range of the quadratic function.
5.f(x) = 7 - (x + 4)2
for any parabola of the form
f(x) = a(x-h)^2 + k
the vertex is (h,k) and the axis of symmetry is x = h
Make use of that fact for #1 and #3
The range is the set of y values that the graph covers.
so in #5 first rewrite it as
f(x) = -(x+4)^2 - 7
Wouldn't the vertex be (-4,-7) and since the parabola opens downwards, what do you thing would be the y values covered by the graph?
Please check my answers.
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
1.f(x) = (x - 4)2 - 4
-I got (4,-4)
Find the axis of symmetry of the parabola defined by the given quadratic function.
3.f(x) = (x + 2)2 + 7
-I got: x=-2
Find the range of the quadratic function.
5.f(x) = 7 - (x + 4)2
I got: (-inifinity,7]
find the coordinates of the vertex for the parabola defined by the given quadratic function f(x)=(x+7)^2-6
Sure, I'd be happy to help you with these problems and explain how to find the answers.
1. To find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = (x - 4)² - 4, you can use the vertex form of a quadratic equation, which is given by y = a(x - h)² + k. In this equation, the vertex of the parabola is represented by the point (h, k).
Comparing this to the given quadratic function, we can identify that h = 4 and k = -4. Therefore, the coordinates of the vertex are (4, -4).
3. The axis of symmetry of a parabola defined by the quadratic function f(x) = (x + 2)² + 7 can be found using the formula x = -b / (2a), where the equation is written in the form y = ax² + bx + c. In this case, a = 1 and b = 2.
Applying the formula, we have x = -2 / (2*1) = -1. Therefore, the axis of symmetry is given by the equation x = -1.
5. To find the range of the quadratic function f(x) = 7 - (x + 4)², we need to determine the set of all possible y-values that the function can take.
In this case, the quadratic term (x + 4)² can only be equal to or greater than 0 since it is a square. Therefore, the y-value will always be 7 minus a non-negative value.
The lowest possible value for (x + 4)² is 0, which gives us a y-value of 7. As the quadratic term increases, the y-value decreases.
So the range of the quadratic function is all real numbers less than or equal to 7. In interval notation, this can be written as (-∞, 7].