Question

5-43.
based on the tables below, what are the x- and y-intercepts of the corresponding graphs? use the
fact that the relationship shown in the table in part (b) is quadratic to write an equation to
represent the relationship. homework help (you can leave the answer in either factored form
or standard form).

Explanation:

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Part a:

Step1: Find x-intercepts (y=0)

Identify rows where $y=0$: $x=3, x=-5$

Step2: Find y-intercept (x=0)

Identify row where $x=0$: $y=16$

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Part b:

Step1: Identify x-intercepts (y=0)

Rows with $y=0$: $x=1, x=2.5$. Write factored quadratic form:
$y=a(x-1)(x-2.5)$

Step2: Solve for $a$ using (0, -2.5)

Substitute $x=0, y=-2.5$:
$-2.5=a(0-1)(0-2.5)$
$-2.5=a(2.5)$
$a=\frac{-2.5}{2.5}=-1$

Step3: Write final quadratic equation

Substitute $a=-1$ into factored form:
$y=-(x-1)(x-2.5)$

Step4: Find intercepts

x-intercepts: $x=1, x=2.5$; y-intercept (set $x=0$): $y=-2.5$

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Part c:

Step1: Find x-intercepts (y=0)

Identify rows where $y=0$: $x=8$

Step2: Find y-intercept (x=0)

Identify row where $x=0$: $y=-16$

Answer:

a.

• x-intercepts: $x=3$, $x=-5$
• y-intercept: $y=16$

b.

• x-intercepts: $x=1$, $x=2.5$
• y-intercept: $y=-2.5$
• Quadratic equation: $y=-(x-1)(x-2.5)$ (or expanded form $y=-x^2+3.5x-2.5$)

c.

• x-intercept: $x=8$
• y-intercept: $y=-16$