Answer: 9 is the value of "x".
Please help me I don't understand this at all and I can't get it. I spent 4 hours on these equations
2 answers:
Answer:
- h(x) = 1/2 |x - 1| - 2
- h(x) = - (x + 2)² + 3
Step-by-step explanation:
- <em>See attached</em>
You need to recognize the parent function by looking at the graph. Then you need to find out how different is the graph from the parent function and finally work out the equation of the graph considering the transformations.
4)
<u>The parent function is the absolute value function:</u>
- h(x) = |x|
Its vertex is at the origin. We see the vertex has shifted and also the slope has changed.
We can find the slope easily, the ratio of rise to run is 1/2
<u>The function becomes:</u>
- h(x) = 1/2 |x|
Now considering the translation. We see the vertex has coordinate of (1, -2)
It means the graph has shifted 1 unit right and 2 units down.
<u>The shift right is shown as:</u>
- h(x) = 1/2 |x - 1|
<u>and adding the shift down:</u>
- h(x) = 1/2|x - 1| - 2
This is our final equation.
5)
Parabola is the graph of the quadratic function.
<u>The vertex form of the function is:</u>
- h(x) = a(x - h)² + k, where (h, k) is the vertex
<u>Now, we see it is opening down and the vertex is at (-2, 3):</u>
- h(x) = a(x - (-2))² + 3 = a(x + 2)² + 3
<u>To find the value of a we can use a point on the graph. Let's use point (0, -1):</u>
- -1 = a(0 + 2)² + 3
- -1 = 4a + 3
- 4a = -4
- a = -1
<u>The function is:</u>
- h(x) = - (x + 2)² + 3
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Answer:
Option (b) is correct.
Step-by-step explanation:
Given expression "four times the square of a number is thirty-six"
We have to write it mathematically and choose the correct options out of given options.
Consider the given expression "four times the square of a number is thirty-six"
Then
let the number be x ,
Then four times the square of a number written mathematically as
And given "four times the square of a number is thirty-six" written mathematically as
Therefore, "four times the square of a number is thirty-six" written mathematically as
Option (b) is correct.
Answer:
(x + 2)²
Step-by-step explanation:
Given
x² + 4x + 4 ← is a perfect square of the form
(x + a)² = x² + 2ax + a²
Compare like terms
a² = 4 ⇒ a = = 2, thus
x² + 4x + 4 = (x + 2)²
1 step: to draw a rectangle around triangle RST, you should
- draw points A(-1,-1), B(-1,3) and C(2,3);
- connect points A, B, C and T consecutively.
2 step: rectangle ABCT has length AB=4 units and width BC=3 units. Then
sq. un.
3 step:
sq. un.
sq. un.
sq. un.
4 step:
sq. un.
Answer: in step two you write dimensions of rectangle ABCT: length 4 units and width 3 units. Correct choice is B.