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Exercises for Question Type 10: Using data points or images to estimate quadratic equations - IB | RevisionDojo

Question 1

Find the equation of the quadratic function with roots $x=-3$ and $x=5$ that passes through the point $(0, -15)$ .

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Question 2

Find the quadratic function $f(x)=ax^2+bx+c$ that passes through the points $(0,1)$ , $(1,3)$ , and $(2,7)$ .

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Question 3

Find the quadratic function $f(x) = ax^2 + bx + c$ that passes through the points $(1, 2)$ , $(3, 10)$ , and $(5, 26)$ .

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Question 4

Express the quadratic function with vertex $(2, 3)$ that passes through $(4, 11)$ in the form $f(x) = a(x - 2)^2 + 3$ .

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Question 5

Find the equation of the quadratic function in standard form given its vertex $(-1,4)$ and $y$ -intercept at $(0,1)$ .

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Question 6

A projectile follows a parabolic path $y=f(x)$ with $f(0)=0$ , $f(2)=6$ , and $f(5)=0$ . Find $f(x)$ .

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Question 7

A parabola is symmetric about $x=3$ , has minimum value $0$ at the vertex, and satisfies $f(1)=8$ . Find $f(x)$ .

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Question 8

The question asks to determine the coefficients of a quadratic function $f(x) = ax^2 + bx + c$ given a set of coordinates in a table.

Given the table of values for $f(x) = ax^2 + bx + c$ :

\begin{array}{|c|c|c|c|} \hline x & -1 & 0 & 1 \\ \hline y & 6 & 1 & 0 \\ \hline \end{array}

Find $f(x)$ .

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Question 9

Determine the quadratic function in vertex form $f(x)=a(x-h)^2+k$ with vertex $(1,-2)$ that passes through the point $(0,1)$ .

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Question 10

Determine the quadratic function through $(-2,9)$ , $(0,1)$ , and $(3,16)$ .

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Question 11

Find the equation of the quadratic function whose graph passes through the points $(2,0)$ , $(4,0)$ , and $(3,5)$ .

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Question 12

Functions: Quadratic functions

The function $f(x)$ is a quadratic function with vertex $(0, 0)$ . Given that $f(2) = 8$ , find an expression for $f(x)$ .

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Question Type 10: Using data points or images to estimate quadratic equations Exercises