Quadratic transformations c11t7

1. write the vertex form of a quadratic equation.

2. name the 3 ways that a parabola changes with different types of "a" values.

3. what does changing the "h" variable do to the graph of a quadratic?

if "h" is positive how does the parabola move? if “h” is negative?

4. what does changing the "k" variable do to the graph of a quadratic?

if "k" is positive how does the parabola move? if “k” is negative?

5. use the description to write the quadratic function in vertex form: the parent function f(x) = x2 is reflected across the x axis and translated 5 units left and 1 unit down to create g.

g(x) =

6. the parent function f(x) = x2 is compressed by a factor of 3 and translated 4 units right and 2 units up to create g(x). write the new function in vertex form.
g(x) =

1. The vertex form of a quadratic equation is f(x) = a(x - h)² + k where (h, k) is the parabola formed by the equation. 2. The value of a affects the shape of the parabola. Three concrete ways showing this are: i. When a is negative ( a < 0), then the parabola opens downward ii. When a is positive ( a > 0), the the parabola opens upward ii. Lastly, when a reduces, the parabola shrinks. And when a increases, the parabola expands as well. 3. Since h directly affects the value of x, then it means that when h is increased by one unit, the parabola moves to the left by one unit. Similarly, if h decreases by 1 unit, it shifts to the right by one unit. Some textbooks call this as the parabola's horizontal shift. 4. The value of k directly affects the movement of the parabola across the y-axis. That means, if k is increased, the parabola goes up. And when k decreases, the graph goes down as well. 5. We have f(x) = 1(x)² as the original function with (h, k) = (0, 0). If we reflect it, across the x-axis, that means we negate the value across. So, we now have a new function, g(x), g(x) = -(x)². Based from the discussion regarding translations, if we move f(x) 5 units to the left, that means we are to increase the value of h by 5. So now, g(x) becomes g(x) = -(x - 5)² Applying the same concept, if we shift the graph 1 unit below, we decrease the value of k by 1. So we now have a final function of g(x) = -(x - 5)² - 1 6. Using the same initial function with 5, we have f(x) = 1(x)² with (h, k) = (0, 0). Now, since f(x) is to be compressed by 3, g(x) becomes g(x) = 1/3(x)² Translating 4 units to the right means decreasing the value of h by 4 and translating 2 units upwards means increasing the value of k by 2. Thus, we have g(x) = 1/3[x - (-4)]² + 2 Simplifying this, we'll have the new function as g(x) = 1/3(x + 4)² + 2

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.

The correct answer is d, hope this