# Grade 10 Math: Quadratic Equations, Graphs, and More Determining Quadratic Equation when Given Roots and a Point

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### Determine the quadratic equation that has the roots $$x = -4$$ and $$x = 3$$

$$X^2+x-12$$
$$X^2+2x-12$$
$$X^2+x-6$$
$$X^2+x+12$$

### Determine the quadratic equation that has the roots $$x = \frac{9}{2}$$ and $$x = \frac{23}{10}$$

$$X^2-\frac{34}{5}x+\frac{7}{20}$$
$$X^2-\frac{34}{4}x+\frac{7}{20}$$
$$X^2-\frac{34}{5}x+\frac{1}{20}$$
$$X^2-\frac{34}{5}x+\frac{3}{20}$$

### Determine the quadratic equation whose roots are -10 and -8 with a vertex of (-9,-1).

$$(x+10)(x+8)$$
$$(x+10)(x-8)$$
$$(x-10)(x+8)$$
$$(x-10)(x-8)$$

### Determine the quadratic equation whose roots are -9 and -3 with a vertex of (-6,-1).

$$\frac{1}{6}(x+3)(x+9)$$
$$\frac{1}{9}(x+3)(x+9)$$
$$\frac{1}{3}(x+3)(x+9)$$
$$\frac{1}{9}(x+1)(x+9)$$