IB Mathematics Applications & Interpretation Question Type 10: Using Data Points or Images to Estimate Quadratic Equations Exercises

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

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

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

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

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

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

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

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

$$\begin{array}{cccc}x& -1& 0& 1\\ y& 6& 1& 0\end{array}$$

Find $f(x)$.

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

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

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

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