Q1 Find the below by the quadratic formula
a. $f(x)=x^{2}-8 x+15$
b. $g(x)=2 x^{2}-4 x-16$

Q2 a. Graph the demand function
$$
Q_{d}=-4 P+0.01 Y-5 P_{r}+10 T
$$
when $Y=8000, P_{r}=8$, and $T=4$.
b. What type of good is the related good?
c. What happens if $T$ increases to 8 , indicating greater preference for the good?
d. Construct the graph along the traditional economic lines with P on the vertical axis and $Q$ on the horizontal axis.
1

Question

Q1 Find the below by the quadratic formula
a. $f(x)=x^{2}-8 x+15$
b. $g(x)=2 x^{2}-4 x-16$

Q2 a. Graph the demand function
$$
Q_{d}=-4 P+0.01 Y-5 P_{r}+10 T
$$
when $Y=8000, P_{r}=8$, and $T=4$.
b. What type of good is the related good?
c. What happens if $T$ increases to 8 , indicating greater preference for the good?
d. Construct the graph along the traditional economic lines with P on the vertical axis and $Q$ on the horizontal axis.
1

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To solve the quadratic equation $f(x) = x^2 - 8x + 15 = 0$, we can factor it as $(x - 3)(x - 5) = 0$. Thus, the solutions are $x = 3$ and $x = 5$. ‖ ‖ step 2 ⋮ For the quadratic equation $g(x) = 2x^2 - 4x - 16 = 0$, we can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 2$, $b = -4$, and $c = -16$. This gives us $x = \frac{4 \pm \sqrt{(-4)^2 - 4(2)(-16)}}{2(2)}$. Simplifying, we find $x = -2$ and $x = 4$. ‖ ∻Answer∻ ⚹ The solutions for $f(x)$ are $x = 3$ and $x = 5$, and for $g(x)$ are $x = -2$ and $x = 4$. ⚹ ∻Key Concept∻ ⚹ Quadratic Equations and Their Solutions ⚹ ∻Explanation∻ ⚹ Quadratic equations can be solved by factoring or using the quadratic formula, leading to the identification of their roots. ⚹ ∻Solution by Steps∻ ‖ step 1 ⋮ To graph the demand function $Q_d = -4P + 0.01Y - 5P_r + 10T$ with the given values $Y = 8000$, $P_r = 8$, and $T = 4$, we substitute these values into the equation: $Q_d = -4P + 0.01(8000) - 5(8) + 10(4)$. ‖ ‖ step 2 ⋮ Calculating the constants, we find $0.01(8000) = 80$, $-5(8) = -40$, and $10(4) = 40$. Thus, the equation simplifies to $Q_d = -4P + 80 - 40 + 40$, which simplifies further to $Q_d = -4P + 80$. ‖ ‖ step 3 ⋮ The graph of this demand function will have a y-intercept at $Q_d = 80$ when $P = 0$ and a slope of -4, indicating that as price increases, quantity demanded decreases. ‖ ‖ step 4 ⋮ The type of good related to this demand function can be inferred from the negative relationship between price and quantity demanded, indicating it is a normal good. ‖ ‖ step 5 ⋮ If $T$ increases to 8, the equation becomes $Q_d = -4P + 0.01(8000) - 5(8) + 10(8)$. This results in an increase in quantity demanded, reflecting a greater preference for the good. ‖ ∻Answer∻ ⚹ The demand function is $Q_d = -4P + 80$, indicating a normal good, and an increase in $T$ leads to an increase in quantity demanded. ⚹ ∻Key Concept∻ ⚹ Demand Functions and Their Graphs ⚹ ∻Explanation∻ ⚹ Demand functions illustrate the relationship between price and quantity demanded, and changes in external factors can shift the demand curve. ⚹◊How do you apply the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, to find the roots of the function $f(x) = x^{2} - 8x + 15$?⍭ Generate me a similar question◊

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