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

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

Given the vertex at $(0,0)$ and that $f(2)=8$, find $f(x)$.

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

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

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

Given the table of values for $f(x)=ax^2+bx+c$:
x | -1 | 0 | 1
y | 6 | 1 | 0,
find $f(x)$.

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

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

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

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

Find the quadratic passing through $(2,0)$, $(4,0)$, and $(3,5)$.

Approximate the quadratic through $(1,2)$, $(3,6)$, and $(5,10)$.