A quadratic expression $\mathrm{f}(x)$ has the property that $\mathrm{f}(x)\leq0$ has solut

Question

A quadratic expression $\mathrm{f}(x)$ has the property that $\mathrm{f}(x)\leq0$ has solution set exactly $-1\leq x\leq3.$ You are also given $\mathrm{f}(0)=-6$. Find $\mathrm{f}(x)$ in factorised and expanded forms. Explain how you know its leading coefficient must be positive.

Accepted Answer

$\mathrm{f}(x)=2(x+1)(x-3)=2x^2-4x-6$.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Solution:

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