Which answer choice describes how the graph of `f(x)=x^{2}` was transformed to create the graph of `h(x)=x^{2}-1`?
5 answers
The graph of `h(x)=x^{2}-1` was shifted down one unit from the graph of `f(x)=x^{2}`.
Which value of `x` is a solution to this equation?
`2x^{2}+6x-20=0`
`2x^{2}+6x-20=0`
Using factoring, we can begin by factoring the equation as:
2x² + 6x - 20 = 0
2(x² + 3x - 10) = 0
2(x + 5)(x - 2) = 0
Now we can use the zero product property and set each factor equal to zero:
x + 5 = 0 or x - 2 = 0
Solving for x, we have:
x = -5 or x = 2
Therefore, the solutions to the equation `2x^{2}+6x-20=0` are x = -5 and x = 2.
2x² + 6x - 20 = 0
2(x² + 3x - 10) = 0
2(x + 5)(x - 2) = 0
Now we can use the zero product property and set each factor equal to zero:
x + 5 = 0 or x - 2 = 0
Solving for x, we have:
x = -5 or x = 2
Therefore, the solutions to the equation `2x^{2}+6x-20=0` are x = -5 and x = 2.
1) Solve `x^{2}-4x-5=0` and enter solutions below.
2) Push the "Graph It" Button to see a graph of `y=x^{2}-4x-5`
2) Push the "Graph It" Button to see a graph of `y=x^{2}-4x-5`
1) First, we can use factoring to rewrite the equation as:
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
Using the zero product property, we can set each factor equal to zero:
x - 5 = 0 or x + 1 = 0
Solving for x, we get:
x = 5 or x = -1
Therefore, the solutions to the equation `x^{2}-4x-5=0` are x = 5 and x = -1.
2) (See graph below)
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
Using the zero product property, we can set each factor equal to zero:
x - 5 = 0 or x + 1 = 0
Solving for x, we get:
x = 5 or x = -1
Therefore, the solutions to the equation `x^{2}-4x-5=0` are x = 5 and x = -1.
2) (See graph below)
1 answer