Step-by-step explanation:
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Using the discriminant of a quadratic equation, if the graph is translated shifted up 4 units, the graph will have no x-intercepts.
<h3>What is the discriminant of a quadratic equation and how does it influence the solutions?</h3>
A quadratic equation is modeled by:
The discriminant is:
The solutions are as follows:
- If , and it has 2 x-intercepts.
- If , it has 1 x-intercept.
- If , it has no x-intercepts.
In this problem, the function is given by:
f(x) = (x + 5)² - 3.
In standard form:
f(x) = x² + 10x + 22.
We want to find coefficient k for which the function has , then:
f(x) = x² + 10x + 22 + k.
The coefficients are a = 1, b = 10, c = 22 + k, hence:
10² - 4(22 + k) < 0
100 - 88 - 4k < 0
4k > 12
k > 3.
Hence, with k = 4, the function is shifted up 4 units, and the graph will have no x-intercepts.
More can be learned about the discriminant of a quadratic equation at brainly.com/question/19776811
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Answer:
x>7
Step-by-step explanation:
First, you take away 6 from both sides, which gives you 4x>-x+35. Then you add x to both sides, which makes it 5x>35. Divide both sides by 5, and you get x>7
Answer:
This equation shows you how financial aid increases $3000 for every additional sibling, starting at $15,000.
Step-by-step explanation:
This equation means that for every sibling there is an additional $3000 in financial aid. When there are no siblings there is an automatic $15000 in financial aid.
Since you can't have "negative number" of siblings, the domain must begin with 0. You can have a lot of siblings, so let's put the end of domain as infinity.
Domain = [0, ∞)
If you substitute in this domain into the equation, the range will be the output. The least will be $15,000 and the most will be infinity as well.
Range = [15000, ∞)
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Look at the exponents for this question. The smaller the exponent the least it is. If by any chance the exponents are the same then look at the numbers in front of it.
Answer:
1.4 * 10^-2
1.4 * 10^-1
1.5 * 10^3
2 * 10^3