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I have a question that asks "By substituting $x=10$ in the equation, find...". This is the formula in the question, which forms a parabola (representing the path of a ball):

$$y=-0.05x^2+x+1.8$$

However, if I attempt to substitute $x=10$, as stated in the question, I get a straight line. For example:

$$y=-0.05\cdot10^2+10+1.8$$ or $$y=-0.5^2+11.8$$

Based on the follow-up questions, I don't believe a straight line is the intended result. What am I doing wrong when substituting $x=10$?

Moko19
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Craig
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  • Yes...for any function, $f(x): \mathbb R \to \mathbb R$, $f(10)$ is a real number. – lulu Sep 08 '22 at 12:52
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    The given equation tells you the height of the ball as a function of the time $x$. When you plug in a specific value of $x$, you're getting the height at a specific time; this is not a function to graph, it's just a number. – Karl Sep 08 '22 at 12:53
  • In general on this site, convention is not to use "$*$" for multiplication, but to use something like "$\cdot$" (in MathJax, that's coded as "\cdot") instead – Moko19 Sep 08 '22 at 12:56
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    @Karl I believe I understand now. So, treat x=10 as a vertical line along the x-axis. Then finding the intercept value? – Craig Sep 08 '22 at 13:01
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    That's right. For any function $f$, the graph of $y=f(x)$ intersects the vertical line $x=a$ at the point $(a,f(a))$. Substituting $a$ for $x$ in the expression $f(x)$ to get the number $f(a)$ is called "evaluating $f$ at $a$". – Karl Sep 08 '22 at 13:03
  • Equation of parabola is a relation between $x$ and $y$, for every value of $x$ you can calculate corresponding value of $y$ and then you can plot that point $(x,y)$ on a coordinate plane. The graph of parabola consists of these points. – Vasili Sep 08 '22 at 13:21

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