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:
4
Step-by-step explanation:
the Fundamental Theorem of Algebra states that for any polynomial of degree n, there are n roots, some of which may be complex
The polynomial shown is of degree 4 ( highest exponent of x )
Hence the polynomial has 4 roots/ zeros
Well, they are equivalent, but I'm not sure if that's exactly what you're asking. :)
Linear equation: y = mx + c
m = slope
c = y-intercept
Answer: sin(x) / cos(x)
Step-by-step explanation: This is just a trigonometric identity you should have memorized :)