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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to write the equation of the quadratic function that passes through the points $(0,0),$ $(2,30),$ and $(7,0).$ Note that the $y-$coordinate of two of the points is $0.$ Therefore, we know that $0$ and $7$ are the $x-$intercepts of the parabola.

$x$ | $y$ |
---|---|

$0$ | $0$ |

$2$ | $30$ |

$7$ | $0$ |

$y=a⋅x(x−7)$

$30=a⋅2(2−7)$

Solve for $a$

SubTermSubtract term

$30=a⋅2(-5)$

MultPosNeg$a(-b)=-a⋅b$

$30=a(-10)$

DivEqn$LHS/(-10)=RHS/(-10)$

$-3=a$

RearrangeEqnRearrange equation

$a=-3$