A quadratic function is defined by p(x)=(x−1)(x+3).

Mathematics

1 answer:

denis-greek [22]2 years ago

7 0

<h3>Explanation:</h3>

y = (x - 1)(x + 3)

Find y intercept:

y = (0 - 1)(0 + 3) ⇒ y = -3

coordinates: (0, -3)

Find x intercept:

(x - 1)(x + 3) = 0 ⇒ x = 1, x = -3

coordinates of x intercept: (1, 0), (-3, 0)

Vertex: x = -b/2a = -2/2(1) = -1

y = (-1 -1)(-1 +3) = -4

coordinates: (-1, -4)

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Given a data set consisting of 33 unique whole number observations, its five-number summary is: [19,32,47,61,77] how many observ

Dafna11 [192]

Given a data set consisting of 33 unique whole number observations, its five-number summary is: [19,32,47,61,77] how many observations are strictly less than 32?

Solution: The five number summary denotes:

Minimum = 19

First Quartile = 32

Median = 47

Third Quartile = 61

Maximum = 77

Since there are an odd number of observations (33) in the data set, the First Quartile (32) must be at the (33+1)/4 = 8.5th position, meaning there are 7 numbers less than 32.

Therefore, there are 7 observations that are strictly less than 32

3 0

3 years ago

Read 2 more answers

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?

Pavel [41]

$\boxed{x_{1}=\frac{-5 + \sqrt{5}}{2}} \\ \\ \\ \boxed{x_{2}=\frac{-5 - \sqrt{5}}{2}}$

<h2>Explanation:</h2>

Using the quadratic formula:

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ Here: \\ \\ f(x) = x^2 + 5x + 5 \\ \\ \\ So: \\ \\ a=1 \\ \\ b=5 \\ \\ c=5 \\ \\ \\ x=\frac{-5 \pm \sqrt{5^2-4(1)(5)}}{2(1)} \\ \\ x=\frac{-5 \pm \sqrt{25-20}}{2} \\ \\ x=\frac{-5 \pm \sqrt{5}}{2} \\ \\ \\ Two \ solutions: \\ \\ \boxed{x_{1}=\frac{-5 + \sqrt{5}}{2}} \\ \\ \\ \boxed{x_{2}=\frac{-5 - \sqrt{5}}{2}}$